Shing-Tung Yau | Academic Influence

Shing-Tung Yau's AcademicInfluence.com Rankings

Shing-Tung Yau

Mathematics

#6

World Rank

#34

Historical Rank

#1

USA Rank

Differential Geometry

#1

World Rank

#2

Historical Rank

#1

USA Rank

Measure Theory

#19

World Rank

#38

Historical Rank

#8

USA Rank

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Mathematics

Shing-Tung Yau's Degrees

PhD Mathematics University of California, Berkeley

Why Is Shing-Tung Yau Influential?

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According to Wikipedia, Shing-Tung Yau is a Chinese-American mathematician and the William Caspar Graustein Professor of Mathematics at Harvard University. In April 2022, Yau retired from Harvard to become a professor of mathematics at Tsinghua University.

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Shing-Tung Yau's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

On The Ricci Curvature of a Compact Kahler Manifold and the Complex Monge-Ampere Equation, I* (1978) (2611)
IEEE Transactions on Pattern Analysis and Machine Intelligence: Special Issue on Perceptual Organization in Computer Vision (1998) (1855)
Lectures on Differential Geometry (1994) (1564)
On the parabolic kernel of the Schrödinger operator (1986) (1534)
Mathematics and its applications (2002) (1434)
Mirror symmetry is T duality (1996) (1403)
On the proof of the positive mass conjecture in general relativity (1979) (1233)
On the existence of hermitian‐yang‐mills connections in stable vector bundles (1986) (971)
Differential equations on riemannian manifolds and their geometric applications (1975) (966)
Harmonic functions on complete riemannian manifolds (1975) (847)
Calabi's conjecture and some new results in algebraic geometry. (1977) (822)
Proof of the positive mass theorem. II (1981) (693)
On the structure of manifolds with positive scalar curvature (1979) (571)
A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces (1982) (556)
Existence of incompressible minimal surfaces and the topology of three - dimensional manifolds with (1979) (555)
Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces (1976) (528)
On the existence of a complete Kähler metric on non‐compact complex manifolds and the regularity of fefferman's equation (1980) (488)
On the Schrödinger equation and the eigenvalue problem (1983) (476)
Conformally flat manifolds, Kleinian groups and scalar curvature (1988) (471)
A GENERAL SCHWARZ LEMMA FOR KAHLER MANIFOLDS. (1978) (468)
Global conformal surface parameterization (2003) (461)
Stringy Cosmic Strings and Noncompact Calabi-Yau Manifolds (1990) (459)
Sasaki–Einstein Manifolds and Volume Minimisation (2006) (427)
Genus zero surface conformal mapping and its application to brain surface mapping (2003) (398)
Mirror symmetry, mirror map and applications to Calabi-Yau hypersurfaces (1993) (397)
Hypersurfaces with constant scalar curvature (1977) (393)
The Geometric Dual of a–Maximisation for Toric Sasaki–Einstein Manifolds (2005) (382)
Curvature estimates for minimal hypersurfaces (1975) (344)
Compact kähler manifolds of positive bisectional curvature (1980) (340)
Submanifolds with Constant Mean Curvature II (1974) (338)
Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature (1982) (319)
Estimates of eigenvalues of a compact Riemannian manifold (1980) (316)
Mirror Principle I (1997) (307)
Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces (1994) (305)
On the regularity of the solution of the n‐dimensional Minkowski problem (1976) (302)
Genus zero surface conformal mapping and its application to brain surface mapping. (2004) (300)
Local mirror symmetry: Calculations and interpretations (1999) (294)
Evolutionary dynamics on any population structure (2016) (293)
Eigenvalues of the laplacian of compact Riemann surfaces and minimal submanifolds (1980) (293)
The theory of superstring with flux on non-Kähler manifolds and the complex Monge-Ampère equation (2006) (292)
Seminar on differential geometry (1982) (291)
Complete Kähler manifolds with zero Ricci curvature. I (1990) (286)
On the regularity of the monge‐ampère equation det (∂2 u/∂xi ∂xj) = f(x, u) (1977) (283)
Essays on mirror manifolds (1992) (281)
Complete affine hypersurfaces. Part I. The completeness of affine metrics (1986) (273)
Kähler-Einstein metrics on complex surfaces withC1>0 (1987) (260)
Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector. (2007) (257)
High-resolution, real-time 3D absolute coordinate measurement based on a phase-shifting method. (2006) (249)
ON THE UPPER ESTIMATE OF THE HEAT KERNEL OF A COMPLETE RIEMANNIAN MANIFOLD (1981) (241)
Topology of three dimensional manifolds and the embedding problems in minimal surface theory (1980) (235)
Discrete Green's Functions (2000) (230)
Mirror symmetry for two parameter models. I (1996) (226)
Isoperimetric constants and the first eigenvalue of a compact riemannian manifold (1975) (225)
A lower bound for the heat kernel (1981) (223)
Harmonic maps and the topology of stable hypersurfaces and manifolds with non-negative ricci curvature (1976) (222)
On univalent harmonic maps between surfaces (1978) (220)
The existence of embedded minimal surfaces and the problem of uniqueness (1982) (220)
Ricci curvature and eigenvalue estimate on locally finite graphs (2010) (217)
Calabi-Yau four-folds for M- and F-theory compactifications (1997) (215)
Ricci curvature of graphs (2011) (215)
Surveys in Differential Geometry (1999) (214)
Connectedness of the boundary in the AdS / CFT correspondence (1999) (213)
Definition of center of mass for isolated physical systems and unique foliations by stable spheres with constant mean curvature (1996) (209)
Nonlinear Analysis In Geometry (1986) (205)
Mirror Principle II (1999) (202)
BPS states, string duality, and nodal curves on K3 (1995) (201)
EXISTENCE OF KAHLER-EINSTEIN METRICS ON COMPLETE KAHLER MANIFOLDS AND THEIR APPLICATIONS TO ALGEBRAIC GEOMETRY (1987) (197)
Complete Kähler manifolds with zero Ricci curvature II (1991) (196)
Multilevel quality-guided phase unwrapping algorithm for real-time three-dimensional shape reconstruction. (2007) (195)
From special Lagrangian to Hermitian–Yang–Mills via Fourier–Mukai transform (2000) (193)
THE CLASSICAL PLATEAU PROBLEM AND THE TOPOLOGY OF THREE-DIMENSIONAL MANIFOLDS (1982) (191)
Differential Geometry: Partial Differential Equations on Manifolds (1993) (185)
Obstructions to the Existence of Sasaki–Einstein Metrics (2006) (183)
Hermitian-Yang-Mills Connection on Non-Kähler Manifolds (1987) (178)
The existence of a black hole due to condensation of matter (1983) (174)
GPU-assisted high-resolution, real-time 3-D shape measurement. (2006) (172)
High dynamic range scanning technique (2008) (170)
Small resolutions of SU(5)-models in F-theory (2011) (164)
Special Lagrangians, stable bundles and mean curvature flow (2001) (164)
An Estimate of the Gap of the First Two Eigenvalues in the Schr (2009) (159)
Positive scalar curvature and minimal hypersurface singularities (2017) (157)
Canonical Metrics on the Moduli Space of Riemann Surfaces II (2004) (153)
Quasilocal mass in general relativity. (2008) (152)
Positivity of the Total Mass of a General Space-Time (1979) (147)
Isometric Embeddings into the Minkowski Space and New Quasi-Local Mass (2008) (146)
Li-Yau inequality on graphs (2013) (146)
Topological string partition functions as polynomials (2004) (141)
Positivity of quasilocal mass. (2003) (140)
Compact manifolds of nonpositive curvature (1972) (139)
Some Remarks on the Quasi - local Mass (1988) (135)
Compact group actions and the topology of manifolds with non-positive curvature (1979) (133)
Smooth static solutions of the Einstein/Yang-Mills equations (1991) (133)
Anomaly cancellation and smooth non-Kähler solutions in heterotic string theory (2006) (132)
Arithmetic properties of mirror map and quantum coupling (1994) (130)
Decay of Solutions of the Wave Equation in the Kerr Geometry (2005) (129)
Cohomology and Hodge Theory on Symplectic Manifolds: III (2009) (127)
On the curvature of compact Hermitian manifolds (1974) (125)
GKZ-Generalized hypergeometric systems in mirror symmetry of Calabi-Yau hypersurfaces (1996) (122)
Lectures on Harmonic Maps (1997) (121)
Local behavior of Hodge structures at infinity (1997) (119)
COMPLETE THREE DIMENSIONAL MANIFOLDS WITH POSITIVE RICCI CURVATURE AND SCALAR CURVATURE (1982) (119)
Mirror principle III (1999) (119)
The Poincaré-Lelong equation on complete Kähler manifolds (1981) (116)
High-speed three-dimensional shape measurement system using a modified two-plus-one phase-shifting algorithm (2007) (116)
The energy and the linear momentum of space-times in general relativity (1981) (113)
A nonlinear elliptic system for maps from Hermitian to Riemannian manifolds and rigidity theorems in Hermitian geometry (1993) (112)
Brain Surface Conformal Parameterization Using Riemann Surface Structure (2007) (112)
Computational Conformal Geometry (2016) (112)
HEAT-EQUATIONS ON MINIMAL SUBMANIFOLDS AND THEIR APPLICATIONS (1984) (111)
SURVEY ON PARTIAL DIFFERENTIAL EQUATIONS IN 3 DIFFERENTIAL GEOMETRY (1982) (111)
Variational Principles for Minkowski Type Problems, Discrete Optimal Transport, and Discrete Monge-Ampere Equations (2013) (111)
Optimal global conformal surface parameterization (2004) (109)
Review of geometry and analysis (2000) (108)
A Geometric View of Optimal Transportation and Generative Model (2017) (107)
Step-sizes for the gradient method (2008) (106)
Proof of the Positive-Action Conjecture in Quantum Relativity (1979) (102)
Eigenvalues of elliptic operators and geometric applications (2004) (102)
Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions (2016) (99)
Taming symplectic forms and the Calabi–Yau equation (2007) (98)
Geometric Understanding of Deep Learning (2018) (97)
Scalar curvature, non-abelian group actions, and the degree of symmetry of exotic spheres (1974) (96)
Upper bound for the first eigenvalue of algebraic submanifolds (1994) (95)
A note on our previous paper: On the existence of Hermitian Yang–Mills connections in stable vector bundles (1989) (95)
Computing Conformal Structure of Surfaces (2002) (95)
Coverings, Heat Kernels and Spanning Trees (1998) (95)
Negative holomorphic curvature and positive canonical bundle (2015) (94)
Balanced metrics on non-Kahler Calabi-Yau threefolds (2008) (94)
Graph homotopy and Graham homotopy (2001) (94)
Existence of black hole solutions for the Einstein-Yang/Mills equations (1993) (93)
Brain Surface Conformal Parameterization With the Ricci Flow (2012) (92)
Geometry, analysis, and algebraic geometry : forty years of the Journal of Differential Geometry (2009) (91)
The equivariant Dehn's lemma and loop theorem (1981) (91)
Mirror maps, modular relations and hypergeometric series II (1995) (90)
Symplectic Conifold Transitions (2002) (89)
Logarithmic Harnack Inequalities (1996) (88)
Mirror symmetry II (1996) (86)
Dual cones and mirror symmetry for generalized Calabi-Yau manifolds (1996) (86)
Higher eigenvalues and isoperimetric inequalities on Riemannian manifolds and graphs (2000) (86)
Complete Kahler manifolds with nonpositive curvature of faster than quadratic decay1 (1977) (86)
Local Heterotic Torsional Models (2008) (85)
A Monge?Ampère-type equation motivated by string theory (2007) (85)
Duality and Fibrations on G_2 Manifolds (2002) (84)
Teichmuller Mapping (T-Map) and Its Applications to Landmark Matching Registration (2014) (84)
Mirror manifolds and topological field theory (1998) (83)
Volumetric Harmonic Map (2003) (82)
The long-time dynamics of Dirac particles in the Kerr-Newman black hole geometry (2000) (81)
Proof That the Bondi Mass is Positive (1982) (81)
Positivity of quasi-local mass II (2004) (81)
Particlelike solutions of the Einstein-Dirac equations (1998) (78)
Optimization of Surface Registrations Using Beltrami Holomorphic Flow (2010) (78)
Elliptic curves, modular forms & Fermat's last theorem : proceedings of a conference held in the Institute of Mathematics of the Chinese University of Hong Kong (1995) (77)
On projectively flat Hermitian manifolds (1994) (77)
COMPACTIFICATION OF NEGATIVELY CURVED COMPLETE KAHLER MANIFOLDS OF FINITE VOLUME (1982) (75)
Independent component analysis-based classification of Alzheimer's disease MRI data. (2011) (74)
Upper Bounds for Eigenvalues of the Discrete and Continuous Laplace Operators (1996) (74)
Homotopy theory for digraphs (2014) (73)
Monodromy calculations of fourth order equations of Calabi-Yau type (2006) (73)
Non-existence of time-periodic solutions of the Dirac equation in a Reissner-Nordström black hole background (1998) (72)
Global Conformal Parameterization (2003) (70)
$(1,1)$ forms with specified Lagrangian phase: a priori estimates and algebraic obstructions (2015) (70)
A generalization of Liu-Yau's quasi-local mass (2006) (70)
Singularities and Gauge Theory Phases (2014) (70)
Eigenvalues of Graphs and Sobolev Inequalities (1995) (69)
A special Lagrangian type equation for holomorphic line bundles (2014) (68)
Homologies of path complexes and digraphs (2012) (68)
Invariant Solutions to the Strominger System on Complex Lie Groups and Their Quotients (2014) (67)
The Existence of Supersymmetric String Theory with Torsion (2004) (66)
Special Polynomial Rings, Quasi Modular Forms and Duality of Topological Strings (2013) (66)
Harnack inequalities for graphs with non-negative Ricci curvature (2012) (64)
Cohomology of digraphs and (undirected) graphs (2015) (63)
The existence of negatively Ricci curved metrics on three manifolds (1986) (63)
Geometry, Analysis and Topology of Discrete Groups (2008) (63)
Non-existence of continuous convex functions on certain Riemannian manifolds (1974) (63)
Smoothing 3-folds with trivial canonical bundle and ordinary double points (1998) (62)
Autoequivalences of derived category of a K3 surface and monodromy transformations (2002) (62)
Differential geometry inspired by string theory (1999) (61)
D5 elliptic fibrations: non-Kodaira fibers and new orientifold limits of F-theory (2011) (61)
Transformation groups and moduli spaces of curves (2011) (61)
On the Fundamental Group of Compact Manifolds of Non-Positive Curvature (1971) (61)
Harmonic mappings and Kähler manifolds (1983) (61)
Nonexistence of time‐periodic solutions of the Dirac equation in an axisymmetric black hole geometry (1999) (60)
Tunneling Topological Vacua via Extended Operators: (Spin-)TQFT Spectra and Boundary Deconfinement in Various Dimensions (2018) (60)
Floer homology and mirror symmetry I (2001) (59)
Decay Rates and Probability Estimates¶for Massive Dirac Particles¶in the Kerr–Newman Black Hole Geometry (2001) (58)
Three dimensional canonical singularity and ﬁve dimensional N = 1 SCFT (2017) (56)
Computing quasiconformal maps using an auxiliary metric and discrete curvature flow (2012) (55)
Calabi-Yau threefolds and complex multiplication (1998) (55)
Three-dimensional shape measurement using a structured light system with dual cameras (2008) (55)
Chiral algebra of the Argyres-Douglas theory from M5 branes (2016) (53)
Singularities and Gauge Theory Phases II (2014) (53)
The unified discrete surface Ricci flow (2014) (51)
A remark on our paper "Negative Holomorphic curvature and positive canonical bundle" (2016) (51)
Generalized Cohomologies and Supersymmetry (2011) (51)
The legacy of Bernhard Riemann after one hundred and fifty years (2016) (51)
A New Model for Elliptic Fibrations with a Rank One Mordell-Weil Group: I. Singular Fibers and Semi-Stable Degenerations (2014) (51)
Geometry of Riemann surfaces and their moduli spaces (2009) (51)
Volumetric harmonic brain mapping (2004) (50)
On the Harnack inequalities of partial differential equations (1994) (50)
Maximal degeneracy points of GKZ systems (1996) (49)
Geometry of three manifolds and existence of Black Hole due to boundary effect (2002) (47)
A Harnack inequality for homogeneous graphs and subgraphs (1994) (47)
Particle-Like Solutions of the Einstein-Dirac-Maxwell Equations (1998) (47)
Asymptotic form of zero energy wave functions in supersymmetric matrix models (1999) (47)
Compact flat Riemannian manifolds (1972) (46)
Affine manifolds, SYZ geometry, and the 'Y' vertex (2004) (46)
Splitting theorem and an algebraic geometric characterization of locally Hermitian symmetric spaces (1993) (46)
Complete manifolds with nonnegative scalar curvature and the positive action conjecture in general relativity. (1979) (45)
Eigenvalues and diameters for manifolds and graphs (1997) (44)
Manifold splines with single extraordinary point (2007) (44)
Volume doubling, Poincaré inequality and Guassian heat kernel estimate for nonnegative curvature graphs (2014) (44)
Shape-Based Diffeomorphic Registration on Hippocampal Surfaces Using Beltrami Holomorphic Flow (2010) (44)
A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory (1998) (43)
Numerical Computation of Surface Conformal Mappings (2012) (43)
Mirror symmetry and integral variations of Hodge structure underlying one-parameter families of Calabi-Yau threefolds (2006) (43)
Conserved Quantities in General Relativity: From the Quasi-Local Level to Spatial Infinity (2013) (43)
Gravitational wave memory in de Sitter spacetime (2015) (43)
The Deformed Hermitian–Yang–Mills Equation in Geometry and Physics (2017) (43)
Elliptic Virasoro Conformal Blocks (2015) (42)
Harnack inequality for non-self-adjoint evolution equations (1995) (42)
Graphs associated with simplicial complexes (2014) (42)
Three dimensional algebraic manifolds with C1 = 0 and χ = −6 (1987) (42)
Lagrangian torus fibration of quintic hypersurfaces I: Fermat quintic case (2001) (41)
Moment Maps, Nonlinear PDE and Stability in Mirror Symmetry, I: Geodesics (2018) (41)
Non-Existence of Black Hole Solutions¶for a Spherically Symmetric, Static Einstein–Dirac–Maxwell System (1998) (41)
Path Complexes and their Homologies (2020) (41)
Shape Analysis of Vestibular Systems in Adolescent Idiopathic Scoliosis Using Geodesic Spectra (2010) (41)
On the isoperimetric inequality for minimal surfaces (1984) (41)
Holomorphic curves in surfaces of general type. (1990) (41)
Homologies of digraphs and Künneth formulas (2017) (40)
Fourier-Mukai Transform and Mirror Symmetry for D-Branes on Elliptic Calabi-Yau (2000) (39)
A Degenerate Monge--Ampère equation and the Boundary Classes of Kähler Cones (2009) (39)
Fourier-Mukai number of a K3 surface (2002) (38)
Picard-Fuchs equations for relative periods and Abel-Jacobi map for Calabi-Yau hypersurfaces (2009) (38)
Surface Quasi-Conformal Mapping by Solving Beltrami Equations (2009) (38)
Toric morphisms and fibrations of toric Calabi-Yau hypersurfaces (2000) (37)
On sampling with Markov chains (1996) (37)
Geometric Accuracy Analysis for Discrete Surface Approximation (2006) (37)
Surface classification using conformal structures (2003) (37)
Three dimensional canonical singularity and five dimensional N$$ \mathcal{N} $$ = 1 SCFT (2017) (37)
Branes, bundles and attractors: Bogomolov and beyond (2006) (37)
Optimal Global Conformal Surface Parameterization for Visualization (2004) (36)
Eigenvalue inequalities for graphs and convex subgraphs (1997) (36)
Volume doubling, Poincaré inequality and Gaussian heat kernel estimate for non-negatively curved graphs (2017) (36)
4d N = 2 SCFT and singularity theory Part I: Classification (2015) (35)
A strong rigidity theorem for a certain class of compact complex analytic surfaces (1985) (35)
Evaluating Quasilocal Energy and Solving Optimal Embedding Equation at Null Infinity (2010) (35)
Constructing balanced metrics on some families of non-Kahler Calabi-Yau threefolds (2008) (35)
Gradient estimates, Harnack inequalities and estimates for heat kernels of the sum of squares of vector fields (1992) (35)
Minimizing Properties of Critical Points of Quasi-Local Energy (2013) (35)
Moduli space of torsional manifolds (2006) (34)
Remarks on conformal transformations (1973) (34)
Incompressible minimal surfaces, three-dimensional manifolds with nonnegative scalar curvature, and the positive mass conjecture in general relativity. (1978) (33)
Quantum tunneling from three-dimensional black holes (2013) (33)
Kummer structures on a K3 surface: An old question of T. Shioda (2002) (33)
Real time solution of nonlinear filtering problem without memory I (2000) (33)
Fibrewise T-duality for D-branes on elliptic Calabi-Yau (2001) (32)
Maximal unipotent monodromy for complete intersection CY manifolds (2000) (32)
Brain Surface Parameterization Using Riemann Surface Structure (2005) (31)
Finite-dimensional filters with nonlinear drift. III: Duncan-Mortensen-Zakai equation with arbitrary initial condition for the linear filtering system and the Benes filtering system (1997) (31)
Null Asymptotics of Solutions of the Einstein-Maxwell Equations in General Relativity and Gravitational Radiation (2010) (31)
Geometric Compression Using Riemann Surface Structure (2003) (31)
Curvature and holomorphic mappings of complete Kähler manifolds (1990) (31)
Remarks on the group of isometries of a Riemannian manifold (1977) (31)
A near optimal algorithm for edge separators (preliminary version) (1994) (31)
Conformal Slit Mapping and Its Applications to Brain Surface Parameterization (2008) (30)
The electromagnetic Christodoulou memory effect and its application to neutron star binary mergers (2011) (30)
A note on small deformations of balanced manifolds (2011) (30)
Existence of Supersymmetric Hermitian Metrics with Torsion on Non-Kaehler Manifolds (2005) (30)
Intrinsic brain surface conformal mapping using a variational method (2004) (30)
Write-A-Video: Computational Video Montage from Themed Text (2020) (30)
Surface parameterization using Riemann surface structure (2005) (30)
Mordell-Weil Torsion, Anomalies, and Phase Transitions (2017) (30)
An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry (2003) (30)
Simplicial Ricci Flow (2013) (29)
4d N=2 SCFT and singularity theory Part II: Complete intersection (2016) (29)
Period integrals of CY and general type complete intersections (2011) (29)
New heterotic non-Kähler geometries (2008) (29)
An Efficient Energy Minimization for Conformal Parameterizations (2017) (29)
Harmonic Mappings and Algebraic Varieties Over Function Fields (1993) (29)
Ricci-flat graphs with girth at least five (2013) (29)
Local Geometry of the G2 Moduli Space (2008) (29)
Some Properties of Matrix Harmonics on S2 (1998) (29)
On the path homology theory of digraphs and Eilenberg–Steenrod axioms (2018) (28)
Localized Donaldson-Thomas theory of surfaces (2017) (28)
Modified Calabi-Yau manifolds with torsion (1998) (28)
Variational Method on Riemann Surfaces using Conformal Parameterization and its Applications to Image Processing (2008) (28)
Good Geometry on the Curve Moduli (2008) (28)
Real Time Solution of the Nonlinear Filtering Problem without Memory II (2008) (28)
Limit of Quasilocal Mass at Spatial Infinity (2009) (27)
Invariant metrics on negatively pinched complete Kähler manifolds (2017) (27)
Erratum: Decay of solutions of the wave equation in the kerr geometry (Communications in Mathematical Physics (2006) 264 (465-503 ) doi:10.1007/s00220-006-1525-8) (2008) (27)
Hyperbolic Harmonic Mapping for Constrained Brain Surface Registration (2013) (27)
Existence of Solutions to Mean Field Equations on Graphs (2019) (27)
Picard number, holomorphic sectional curvature, and ampleness (2012) (27)
Finite Dimensional Filters with Nonlinear Drift, XI: Explicit Solution of the Generalized Kolmogorov Equation in Brockett–Mitter Program☆☆☆ (1998) (27)
Fourier-Mukai partners of a K3 surface of Picard number one (2002) (27)
Ae-OT: a New Generative Model based on Extended Semi-discrete Optimal transport (2020) (26)
Reducing the Symmetric Matrix Eigenvalue Problem to Matrix Multiplications (1993) (26)
Perfect state transfer on graphs with a potential (2016) (26)
Quantum statistics and spacetime surgery (2016) (26)
Curvatures of moduli space of curves and applications (2013) (26)
Obstacle problem for von Kármán equations (1992) (26)
Special Lagrangian fibrations II: Geometry. A survey of techniques in the study of special Lagrangian fibrations (2001) (26)
4d N=2 SCFT from Complete Intersection Singularity (2016) (26)
Mirror symmetry for hyper-Kähler manifolds (1998) (26)
Goodness of canonical metrics on the moduli space of Riemann surfaces (2014) (25)
Brain Surface Conformal Parameterization with Algebraic Functions (2006) (25)
Path homology theory of multigraphs and quivers (2018) (25)
Shape Analysis by Conformal Modules (2008) (25)
Argyres-Douglas matter and N=2 dualities (2017) (25)
A Rigorous Treatment of Energy Extraction from a Rotating Black Hole (2007) (25)
On some problems in several complex variables and CR geometry (2001) (25)
A Note on ODEs from Mirror Symmetry (1994) (25)
Intrinsic measures of compact complex manifolds (1975) (25)
Pretty good quantum state transfer in symmetric spin networks via magnetic field (2017) (25)
Geometry of three manifolds and existence of Black Hole due to boundary effect (2001) (25)
Seminar on Differential Geometry. (AM-102) (1982) (24)
Li-Yau inequality for unbounded Laplacian on graphs (2018) (24)
Spectral inequalities for partial differential equations and their applications (2012) (24)
Quasilocal angular momentum and center of mass in general relativity (2013) (24)
Spanning trees and random walks on weighted graphs (2015) (24)
Local mirror symmetry at higher genus (2001) (24)
Slit Map: Conformal Parameterization for Multiply Connected Surfaces (2008) (24)
Nested Hilbert schemes on surfaces: Virtual fundamental class (2017) (23)
Azumaya-type noncommutative spaces and morphisms therefrom: Polchinski's D-branes in string theory from Grothendieck's viewpoint (2007) (23)
Convergence of an iterative algorithm for Teichmüller maps via harmonic energy optimization (2015) (23)
Non-Kähler SYZ Mirror Symmetry (2014) (23)
The Role of Partial Differential Equations in Differential Geometry (2010) (23)
c = 2 Rational Toroidal Conformal Field Theories via the Gauss Product (2002) (23)
Linear waves in the Kerr geometry: A mathematical voyage to black hole physics (2008) (23)
Quantum statistics and spacetime topology: Quantum surgery formulas (2019) (23)
Fundamentals of Computational Conformal Geometry (2010) (22)
Perspectives in Mathematical Physics (1994) (22)
Classification of c=2 Rational Conformal Field Theories via the Gauss Product (2002) (22)
Shape Analysis of Planar Multiply-Connected Objects Using Conformal Welding (2014) (22)
Isoperimetric properties of higher eigenvalues of elliptic operators (2003) (22)
Geometric singularities and spectra of Landau-Ginzburg models (1991) (22)
DETECTION OF SHAPE DEFORMITIES USING YAMABE FLOW AND BELTRAMI COEFFICIENTS (2010) (21)
Shafarevich's Conjecture for CY Manifolds I (2003) (21)
Discrete Green's functions and random walks on graphs (2013) (21)
A Degeneration formula of Gromov-Witten invariants with respect to a curve class for degenerations from blow-ups (2004) (21)
On a cohomology of digraphs and Hochschild cohomology (2016) (21)
3 D Harmonic Mapping and Tetrahedral Meshing of Brain Imaging Data (2004) (21)
Recent Development on the Geometry of the Teichmuller and Moduli Spaces of Riemann Surfaces and Polarized Calabi-Yau Manifolds (2009) (21)
Sharp Davies–Gaffney–Grigor’yan Lemma on graphs (2016) (21)
The interaction of Dirac particles with non-abelian gauge fields and gravity – bound states (2000) (21)
Graph Laplacians, Riemannian manifolds, and their machine-learning (2020) (21)
Period Integrals and Tautological Systems (2011) (21)
Ordinary differential equations (1998) (20)
Mathematics: Its content, methods, and meaning (2014) (20)
A Novel Stretch Energy Minimization Algorithm for Equiareal Parameterizations (2017) (20)
The strong rigidity of locally symmetric complex manifolds of rank one and finite volume (1986) (20)
Eigenvalues of Laplacians and other geometric operators (2004) (20)
Calabi-Yau Varieties and Pencils of K3 Surfaces (1996) (20)
Evaluating Small Sphere Limit of the Wang–Yau Quasi-Local Energy (2015) (20)
Absolute phase-assisted three-dimensional data registration for a dual-camera structured light system. (2008) (20)
Uniform texture synthesis and texture mapping using global parameterization (2005) (20)
Mahler’s measure and -series of 3 hypersurfaces (2006) (20)
On the Validity of the Definition of Angular Momentum in General Relativity (2014) (19)
A survey of Calabi-Yau manifolds (2008) (19)
Perspectives on geometric analysis (2006) (19)
Computing Conformal Invariants: Period Matrices (2003) (19)
Yukawa Couplings on Quintic Threefolds (2006) (19)
Mode Collapse and Regularity of Optimal Transportation Maps (2019) (19)
Davies-Gaffney-Grigor'yan Lemma on Graphs (2014) (19)
Calabi–Yau Volumes and Reflexive Polytopes (2017) (19)
ADE string chains and mirror symmetry (2017) (19)
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New N = 2 dualities (2016) (16)
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Chen Ning Yang: A Great Physicist of the Twentieth Century (1995) (16)
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A simple proof of Bogomolov's Theorem on class $\nabla II_{0}$ surfaces with $b_{2} = 0^{1}$ (1990) (15)
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Airy Equation for the Topological String Partition Function in a Scaling Limit (2015) (15)
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Geometry of special holonomy and related topics (2011) (15)
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D-branes and Azumaya noncommutative geometry: From Polchinski to Grothendieck (2010) (15)
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The Positive Mass Theorem with Arbitrary Ends (2021) (15)
Orbifold Euler characteristic (1996) (14)
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Recent Advances in Computational Conformal Geometry (2009) (14)
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A Novel Algorithm for Volume-Preserving Parameterizations of 3-Manifolds (2019) (14)
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Quantum Tunneling on Graphs (2011) (13)
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Homology of path complexes and hypergraphs (2019) (13)
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Calabi-Yau modular forms in limit: Elliptic Fibrations (2015) (13)
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High performance computing for spherical conformal and Riemann mappings (2014) (12)
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Geometric Inequalities for Quasi-Local Masses (2019) (11)
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A note on enumerating rational curves in a K3 surface (2002) (10)
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A brief review on geometry and spectrum of graphs (2012) (9)
Mirror Principle IV (2000) (9)
Generic nonsinusoidal phase error correction for 3D shape measurement using a digital video projector (2006) (9)
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Poisson metrics on flat vector bundles over non-compact curves (2014) (9)
Heterotic String Compactification and New Vector Bundles (2014) (9)
Chapter IX Group Actions on R3 (1984) (9)
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Mirror Principle: A Survey (1998) (9)
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Geometry and Nonlinear Partial Differential Equations (2002) (7)
The positive mass theorem in general relativity (2002) (7)
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Introduction to the cohomology of arithmetic groups (2006) (7)
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Multiresolution Computation of Conformal Structures of Surfaces (1996) (7)
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New definition of quasilocal mass and its positivity (2003) (7)
Exceptional mirror symmetry (2001) (7)
New results on the geometry of the moduli space of Riemann surfaces (2008) (7)
Differential Geometry: Riemannian Geometry (1993) (7)
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Introduction to modern mathematics (2015) (7)
Semicontinuity of 4d N = 2 spectrum under renormalization group (cid:13)ow (2016) (7)
Positive Scalar Curvature on Noncompact Manifolds and the Liouville Theorem. (2020) (7)
An introduction to mirror manifolds (1998) (7)
An application of eigenvalue estimate to algebraic curves defined by congruence subgroups (1996) (7)
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Jordan structures in Banach manifolds (2001) (6)
Local mass in general relativity (2008) (6)
Cohomology of groups and algebraic K-theory (2010) (6)
Tsing Hua Lectures on Geometry & Analysis (1997) (6)
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Global shifted potentials for moduli spaces of sheaves on CY4 (2019) (5)
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Handbook of group actions. Volume III (2018) (5)
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DGBV algebras and mirror symmetry (2001) (5)
The Ornstein-Uhlenbeck process on a Riemannian manifold (2001) (5)
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A New Approach to Sparse Matrix Eigenvalues (1993) (5)
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A Construction of stable bundles and reflexive sheaves on Calabi-Yau threefolds (2014) (5)
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Conformal Surface Morphing with Applications on Facial Expressions (2015) (5)
Atiyah class and sheaf counting on local Calabi Yau fourfolds (2018) (5)
A Note on the Total Curvature of a Kähler Manifold (1996) (5)
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Piecewise function generated by the solutions of linear ordinary differential equation (2008) (5)
Cayley-Bacharach property and -very ampleness (2001) (5)
The Candelas-de la Ossa-Green-Parkes formula (1998) (5)
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Mahler measure variations, Eisenstein series and instanton expansions (2006) (5)
Optimal mass transport for geometric modeling based on variational principles in convex geometry (2014) (5)
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Quasi-local mass on unit spheres at spatial infinity (2019) (4)
Recent development of computational conformal geometry (2012) (4)
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General flattened Jaffe models for galaxies (2002) (4)
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Real time algorithm for nonlinear filtering problem (2001) (4)
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Melvin-Morton conjecture: A survey (2001) (3)
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Topological and Geometric Tools for the Analysis fo Complex Networks (2013) (0)
Workshop on Geometric Flows (2006) (0)
Lectures on Geometry and Topology held at Harvard University, May 3-5, 1996 (1998) (0)
D-branes and synthetic/$C^{\infty}$-algebraic symplectic/calibrated geometry, I: Lemma on a finite algebraicness property of smooth maps from Azumaya/matrix manifolds (2015) (0)
A G ] 1 A ug 2 01 9 GLOBAL SHIFTED POTENTIALS FOR MODULI SPACES OF SHEAVES ON CALABI-YAU FOUR-FOLDS (2019) (0)
Symplectic forms, 2+1 soliton equations, and supersymmetric gauge theories (2001) (0)
Comment on: Positivity of quasilocal mass. Authors' reply (2004) (0)
D G ] 1 J an 2 01 6 THE REST MASS OF AN ASYMPTOTICALLY ANTI-DE SITTER SPACETIME (2018) (0)
Long time behavior of curves evolving by curvature (2001) (0)
From the great wall to the great collider (2015) (0)
Sharp Davies–Gaffney–Grigor’yan Lemma on graphs (2017) (0)
Wellposedness of the two and three dimensional full water wave problem (2012) (0)
A survey on retrograde and prograde orbits of the three-body problem by variational methods (2012) (0)
Existence of solutions to time dependent parabolic equations with unbounded coefficients: application to Duncan-Mortensen-Zakai equations (2000) (0)
Strong embeddings and $2$-isomorphism (2016) (0)
SHIING-SHEN CHERN (1911-2004) (2011) (0)
A G ] 8 J ul 2 00 2 COUNTING FOURIER-MUKAI PARTNERS AND APPLICATIONS (2008) (0)
Airy Equation for the Topological String Partition Function in a Scaling Limit (2016) (0)
Holographic duals of 4D field theories (2003) (0)
Introduction to enumerative invariants (1998) (0)
A G ] 1 S ep 2 02 1 Semiorthogonal decomposition of D b ( Bun L 2 ) (2021) (0)
A note on balanced metrics under small deformations (2011) (0)
Minimal Path and Acyclic Models (2022) (0)
One hundred years of general relativity : a jubilee volume on general relativity and mathematics (2015) (0)
Intermittent Behaviors in Coupled Piecewise Expanding Map Lattices (2021) (0)
Complete cscK Metrics on the Local Models of the Conifold Transition (2015) (0)
The Shape of a Life (2019) (0)
Mirror symmetry: aspects of the first 10 years (2003) (0)
A modular non-rigid Calabi-Yau threefold (2006) (0)
Spectral theory and geometry of locally symmetric spaces (2001) (0)
JHEP 4 d N = 2 SCFT and singularity theory Part I : Classification (2018) (0)
H eterotic K (cid:127)ahler/non-K (cid:127)ahler Transitions (2013) (0)
Some progress on computational geometry (2012) (0)
[Mathematics and string theory]. Progress report [August 1, 1992--July 31, 1993] (1993) (0)
Strictification and gluing of Lagrangian distributions on derived schemes with shifted symplectic forms (2019) (0)
Rational curves and classification of algebraic varieties (1998) (0)
6. The War and Its Aftermath: Andrew Gleason, George Mackey, and an Assignation in Hilbert Space (2013) (0)
Topics on geometric analysis (2012) (0)
An update on (small) quantum cohomology (1998) (0)
Discovering hierarchical structures in weighted graphs using Ricci-flow method (2020) (0)
Supertranslation invariance of angular momentum at null infinity in double null gauge (2022) (0)
Introduction to duality (1996) (0)
1 Essential mathematical backgrounds for physicists (2021) (0)
Epilogue: Numbers and Beyond (2013) (0)
Variational construction of diffusion orbits in convex Hamiltonian systems with multiple degrees of freedom (2008) (0)
Special subvarieties of _{ℊ} (2008) (0)
Eta invariants for even dimensional manifolds (2012) (0)
A G ] 4 N ov 2 01 8 DIFFERENTIAL ZEROS OF PERIOD INTEGRALS AND GENERALIZED HYPERGEOMETRIC FUNCTIONS (2018) (0)
Extremal Bundles on Calabi–Yau Threefolds (2015) (0)
Topology evolutions of silhouettes (2007) (0)
A note on the topology of the boundary in the AdS/CFT correspondence (2003) (0)
$\ell$-adic Tautological Systems (2021) (0)
Two-dimensional Riemann problems for conservation laws in gas dynamics (2001) (0)
Vector bundles on non-primary Hopf manifolds with abelian fundamental group (2008) (0)
The Landau-Lifshitz equation and its gauge equivalent structure (2002) (0)
On the modularity of Calabi-Yau threefolds containing elliptic ruled surfaces Appendix A. A Modularity Criterion for Integral Galois Representations and Calabi-Yau Threefolds (2006) (0)
Techniques for the Analytic Proof of the Finite Generation of the Canonical Ring (2008) (0)
Proceedings of the Conference on Strings, Duality, and Geometry Centre de Recherches Mathématiques of the Université de Montréal (CRM), March 2000 (2002) (0)
Integrable connections and Galois representations (2012) (0)
Regularity of Einstein spacetimes (2012) (0)
The Mathematics of Richard Schoen (2018) (0)
Separating and extending subgroups of a locally compact group (2008) (0)
REVIEWS AND DESCRIPTIONS OF TABLES AND BOOKS (1990) (0)
A Brief History of Kähler Geometry (2015) (0)
D-type fiber-base duality (2018) (0)
3D Technology and Its Impact on the Future of Technology (2015) (0)
Mathematics, mathematics education and the mouse (2008) (0)
Homologies of digraph (2012) (0)
Mirror symmetry in higher and lower dimensions (Part IV) (1996) (0)
Formation of trapped surfaces in the Einstein-Yang-Mills system (2023) (0)
The address on the celebration for the 100th birthday of Professor Su Buqing (2002) (0)
A Two-Phase Optimal Mass Transportation Technique for 3D Brain Tumor Detection and Segmentation (2021) (0)
Moment Maps, Nonlinear PDE and Stability in Mirror Symmetry, I: Geodesics (2021) (0)
Mathematics and string theory (1993) (0)
Calculus of operator functions (2010) (0)
Mathematics, Physics, and Calabi-Yau Manifolds (2013) (0)
Conserved quantities in general relativity -- the view from null infinity (2022) (0)
Dynamics of shock fronts for some hyperbolic systems (2012) (0)
4. Analysis and Algebra Meet Topology: Marston Morse, Hassler Whitney, and Saunders Mac Lane (2013) (0)
On the correspondence between D-branes and stationary supergravity solutions of type II Calabi-Yau compactifications (2003) (0)
Real-time numerical solution to Duncan-Mortensen-Zakai equation (2001) (0)
3. The Dynamical Presence of George David Birkhoff (2013) (0)

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