Kefeng Liu | Academic Influence

Kefeng Liu's AcademicInfluence.com Rankings

Kefeng Liu

Mathematics

#312

World Rank

#665

Historical Rank

#149

USA Rank

Measure Theory

#1269

World Rank

#1609

Historical Rank

#459

USA Rank

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Mathematics

Kefeng Liu's Degrees

PhD Mathematics Princeton University
Bachelors Mathematics Peking University

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Why Is Kefeng Liu Influential?

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According to Wikipedia, Kefeng Liu , is a Chinese-American mathematician who is known for his contributions to geometric analysis, particularly the geometry, topology and analysis of moduli spaces of Riemann surfaces and Calabi–Yau manifolds. He is a professor of mathematics at University of California, Los Angeles, as well as the executive director of the Center of Mathematical Sciences at Zhejiang University. He is best known for his collaboration with Bong Lian and Shing-Tung Yau in which they establish some enumerative geometry conjectures motivated by mirror symmetry.

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Kefeng Liu'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

Mirror Principle II (1999) (202)
On the asymptotic expansion of Bergman kernel (2004) (182)
A Proof of a Conjecture of Marino-Vafa on Hodge Integrals (2003) (158)
A mathematical theory of the topological vertex (2004) (156)
Canonical Metrics on the Moduli Space of Riemann Surfaces II (2004) (153)
On modular invariance and rigidity theorems (1995) (103)
A formula of two-partition Hodge integrals (2003) (75)
Geometry of Hermitian manifolds (2010) (75)
Ricci Curvatures on Hermitian manifolds (2014) (74)
On a proof of the Labastida-Marino-Ooguri-Vafa conjecture (2007) (72)
Modular invariance and characteristic numbers (1994) (72)
On elliptic genera and theta-functions (1996) (70)
Geometry, Analysis and Topology of Discrete Groups (2008) (63)
Heat kernel and moduli spaces II (1996) (61)
Topological string partition functions as equivariant indices (2004) (58)
Geometric Height Inequalities (1996) (56)
Wave character of metrics and hyperbolic geometric flow (2007) (50)
Positivity and vanishing theorems for ample vector bundles (2010) (49)
Mariño-Vafa formula and Hodge integral identities (2003) (45)
Hyperbolic Mean Curvature Flow (2010) (44)
On family rigidity theorems, I (1999) (44)
Recursion Formulae of Higher Weil–Petersson Volumes (2007) (42)
Quasi-isometry and deformations of Calabi–Yau manifolds (2012) (40)
HYPERBOLIC MEAN CURVATURE FLOW: EVOLUTION OF PLANE CURVES (2008) (37)
A simple proof of Witten conjecture through localization (2005) (36)
A proof of the Faber intersection number conjecture (2008) (36)
Localization, Hurwitz Numbers and the Witten Conjecture (2006) (35)
Curvatures of direct image sheaves of vector bundles and applications I (2013) (31)
Global existence of smooth solutions to two-dimensional compressible isentropic Euler equations for Chaplygin gases (2010) (30)
The Hyperbolic Geometric Flow on Riemann Surfaces (2007) (30)
Mean Curvature Flow of Higher Codimension in Hyperbolic Spaces (2011) (30)
The extension and convergence of mean curvature flow in higher codimension (2011) (29)
Hyperbolic Geometric Flow (I): Short-time Existence and Nonlinear Stability (2006) (29)
Good Geometry on the Curve Moduli (2008) (28)
Some remarks on circle action on manifolds (2010) (26)
Remarks on the Cartan Formula and Its Applications (2011) (26)
Curvatures of moduli space of curves and applications (2013) (26)
Holomorphic equivariant cohomology (1995) (26)
Rigidity and vanishing theorems in $K$-theory (1999) (26)
New Structure of Knot Invariants (2010) (26)
Goodness of canonical metrics on the moduli space of Riemann surfaces (2014) (25)
On orbifold elliptic genus (2001) (25)
A REMARK ON 'SOME NUMERICAL RESULTS IN COMPLEX DIFFERENTIAL GEOMETRY' (2006) (23)
$Spin^c$ manifolds and rigidity theorems in $K$-theory (2000) (22)
Elliptic Genus and Vertex Operator Algebras (2002) (22)
MODULAR FORMS AND TOPOLOGY (1996) (22)
Recent Development on the Geometry of the Teichmuller and Moduli Spaces of Riemann Surfaces and Polarized Calabi-Yau Manifolds (2009) (21)
Hermitian Harmonic maps and non-degenerate curvatures (2014) (21)
Shafarevich's Conjecture for CY Manifolds I (2003) (21)
Elliptic genus and η-invariant (1994) (19)
Heat kernels, symplectic geometry, moduli spaces, and finite groups (1999) (19)
Chern forms of holomorphic Finsler vector bundles and some applications (2015) (19)
Adiabatic Limits and Foliations (1999) (19)
Dissipative Hyperbolic Geometric Flow (2007) (19)
HEAT KERNEL AND MODULI SPACE (2004) (19)
The S 1 fixed points in Quot-schemes and mirror principle computations (2001) (18)
Mirzakharni's recursion formula is equivalent to the Witten-Kontsevich theorem (2007) (17)
Formal pseudodifferential operators and Witten's r-spin numbers (2011) (16)
Time-periodic solutions of the Einstein’s field equations I: general framework (2008) (16)
On mod 2 and higher elliptic genera (1992) (16)
A REMARK ON WEIGHTED BERGMAN KERNELS ON ORBIFOLDS (2011) (16)
Life-Span of Classical Solutions to Hyperbolic Geometric Flow in Two Space Variables with Slow Decay Initial Data (2010) (16)
Geometry of logarithmic forms and deformations of complex structures (2017) (16)
Mean curvature flow of higher codimension in Riemannian manifolds (2012) (15)
Four proofs for the Cheeger inequality and graph partition algorithms (2010) (15)
Congruent skein relations for colored HOMFLY-PT invariants and colored Jones polynomials (2014) (15)
Geometric aspects of the moduli space of riemann surfaces (2004) (15)
New properties of the intersection numbers on moduli spaces of curves (2006) (14)
Modular forms and generalized anomaly cancellation formulas (2011) (14)
Time-periodic solutions of the Einstein’s field equations II: geometric singularities (2008) (13)
Descendent integrals and tautological rings of moduli spaces of curves (2009) (13)
A SIMPLE PROOF OF MIRZAKHANI’S RECURSION FORMULA OF WEIL-PETERSSON VOLUMES (2009) (12)
Automorphic forms and the Langlands program (2010) (12)
Logarithmic vanishing theorems on compact Kähler manifolds I (2016) (11)
The flabby class group of a finite cyclic group (2010) (11)
Rigidity of higher elliptic genera (1996) (11)
Generalized Ricci flow I: Local existence and uniqueness (2008) (11)
The n-point functions for intersection numbers on moduli spaces of curves (2007) (11)
Minimal Complex Surfaces with Levi–Civita Ricci-flat Metrics (2017) (11)
Global Torelli Theorem for Projective Manifolds of Calabi-Yau Type (2012) (10)
S 1 -fixed-points in hyper-Quot-schemes and an exact mirror formula for flag manifolds from the extended mirror principle diagram (2004) (10)
On Elliptic Genera and Foliations (1999) (10)
Levi-Civita Ricci-flat metrics on compact complex manifolds (2018) (10)
On an algebraic formula and applications to group action on manifolds (2011) (9)
Mirror Principle: A Survey (1998) (9)
Geodesic-Einstein metrics and nonlinear stabilities (2017) (9)
Mirror Principle IV (2000) (9)
Selected expository works of Shing-Tung Yau with commentary (2014) (9)
CIRCLE ACTION AND SOME VANISHING RESULTS ON MANIFOLDS (2010) (9)
Remarks on the geometry of moduli spaces (1996) (9)
A remark on Mirzakhani's asymptotic formulae (2011) (8)
Compact K\"ahler manifolds with positive orthogonal bisectional curvature (2017) (8)
Virasoro constraints and Hurwitz numbers through asymptotic analysis (2009) (8)
HEAT KERNEL AND MODULI SPACES (1996) (8)
Hodge metric completion of the moduli space of Calabi-Yau manifolds (2013) (8)
On SL2(Z) and Topology (1994) (8)
Computing top intersections in the tautological ring of $${\mathcal{M}_g}$$ (2010) (7)
A geometric heat flow for vector fields (2011) (7)
Mathematical results inspired by physics (2003) (7)
On A-twisted moduli stack for curves from Witten's gauged linear sigma models (2002) (7)
Gravitational anomaly cancellation and modular invariance (2010) (7)
New results on the geometry of the moduli space of Riemann surfaces (2008) (7)
Anomaly Cancellation and Modularity (2012) (7)
From local Torelli to global Torelli (2015) (7)
A Donaldson type functional on a holomorphic Finsler vector bundle (2015) (7)
A note on modular forms and generalized anomaly cancellation formulas (2011) (7)
Finiteness of Subfamilies of Calabi-Yau n-Folds over Curves with Maximal Length of Yukawa-Coupling (2010) (7)
Rigidity Theorems on Odd Dimensional Manifolds (2009) (7)
Effective vanishing theorems for ample and globally generated vector bundles (2013) (7)
Cohomology of groups and algebraic K-theory (2010) (6)
$K$-theory associated to vertex operator algebras (2004) (6)
A Survey of Mirror Principle (2000) (6)
Time-periodic solutions of the Einstein’s field equations III: physical singularities (2011) (6)
Volume conjecture for $SU(n)$-invariants (2015) (6)
Solving equations with Hodge theory (2018) (6)
A Global Torelli Theorem for Calabi-Yau Manifolds (2011) (5)
The deformation of pairs $(X, E)$ lifting from base family (2018) (5)
The Candelas-de la Ossa-Green-Parkes formula (1998) (5)
Hirzebruch Xy genera of the Hilbert schemes of surfaces by localization formula (2002) (5)
Complex Finsler vector bundles with positive Kobayashi curvature (2018) (5)
Adiabatic limits, vanishing theorems and the noncommutative residue (2006) (5)
New results of intersection numbers on moduli spaces of curves (2007) (5)
Cubic forms, anomaly cancellation and modularity (2020) (4)
Recent results on the moduli spaces of Riemann surfaces (2005) (4)
On $\bold{SL_2(Z)}$ and Topology (1994) (4)
Intersection numbers and automorphisms of stable curves (2006) (4)
Harmonic maps between compact Hermitian manifolds (2008) (4)
Cyclotomic expansions for the colored HOMFLY-PT invariants of double twist knots (2021) (4)
New proofs of the Torelli theorems for Riemann surfaces (2012) (4)
Remarks on BCOV invariants and degenerations of Calabi-Yau manifolds (2018) (4)
Boundedness of the images of period maps and applications (2015) (4)
An effective recursion formula for computing intersection numbers (2007) (4)
Geometry of complex bounded domains with finite-volume quotients (2018) (4)
Applications of the Affine Structures on the Teichmüller Spaces (2014) (4)
A New Approach to Deriving Recursion Relations for the Gromov-Witten Theory (2008) (3)
New structure for orthogonal quantum group invariants (2013) (3)
Moduli spaces as ball quotients I, local theory (2018) (3)
Rigidity and Vanishing Theorems in K-Theory II (2000) (3)
On Family Rigidity Theorems II (1999) (3)
Localization and Conjectures from String Duality (2006) (3)
Deformations of complex orbifolds and the period maps (2018) (3)
Arithmetic groups, mapping class groups, related groups, and their associated spaces (2010) (3)
Deforming submanifolds of arbitrary codimension in a sphere (2012) (3)
REMARKS ON NONABELIAN LOCALIZATION (2002) (3)
Toric Sasaki-Einstein geometry (2010) (3)
Hodge theory and deformations of K\"ahler manifolds (2012) (2)
Recursions and asymptotics of intersection numbers (2016) (2)
Anomaly cancellation and modularity, II: The E8 ×E8 case (2017) (2)
Heat kernel coefficients on Kahler manifolds (2013) (2)
Computing top intersections in the tautological ring of M g (2012) (2)
Zeta functions in combinatorics and number theory (2010) (2)
Global methods of solving equations on manifolds (2018) (2)
Number-theoretic techniques in the theory of Lie groups and differential geometry (2010) (2)
Anomaly cancellation and modularity, II: The E8 ×E8 case (2017) (2)
The Ricci flow and geometrization of three-manifolds (2010) (2)
Logarithmic vanishing theorems for effective q-ample divisors (2018) (2)
A new kind of solutions of the Einstein's field equations with non-vanishing cosmological constant (2009) (1)
Number theory, ancient and modern (2010) (1)
RELATIONS AMONG FIXED POINTS (2002) (1)
Quantum Correction and the Moduli Spaces of Calabi-Yau Manifolds (2014) (1)
Global Torelli Theorem for Teichmuller Spaces of Polarized Calabi-Yau manifolds (2009) (1)
Book Review: Modular Calabi-Yau threefolds (2007) (1)
Vanishing Theorems for Sheaves of Logarithmic Differential Forms on Compact Kähler Manifolds (2022) (1)
Hodge metric completion of the Teichm\"uller space of Calabi-Yau manifolds (2013) (1)
LOCALIZATION AND STRING DUALITY (2005) (1)
Canonical sections of Hodge bundles on moduli spaces (2020) (1)
2 5 A ug 2 00 3 Shafarevich ’ s Conjecture for CY Manifolds I ( Moduli of CY Manifolds ) (2008) (1)
Algebraicity of the image of period map (2016) (1)
Boundedness of the period maps and global Torelli theorem (2017) (1)
Anomaly Cancellation and Modularity. II: $E_8\times E_8$ case (2012) (1)
J ul 2 01 2 HODGE THEORY AND DEFORMATIONS OF KÄHLER MANIFOLDS (2012) (1)
Simultaneous normalization of period map and affine structures on moduli spaces (2019) (1)
Local-global principles (2010) (1)
Positive Kobayashi curvature metrics on ample vector bundles (2018) (1)
On some topics in automorphic representations (2010) (1)
Calculus of operator functions (2010) (0)
1 S ep 2 00 1 On orbifold elliptic genus (2002) (0)
Modular Forms and Anomaly Cancellations in String Theory and M-Theory (2021) (0)
Ja n 20 02 Elliptic genus and vertex operator algebras (2008) (0)
Hyperbolic Gradient Flow: Evolution of Graphs in R^{n+1} (2010) (0)
VIRASORO CONSTRAINTS AND HURWITZ NUMBERS THROUGH ASYMPTOTIC (2009) (0)
An affine sphere equation associated to Einstein toric surfaces (2010) (0)
A ug 2 00 4 A MATHEMATICAL THEORY OF THE TOPOLOGICAL VERTEX (2008) (0)
The adaptive PML method for acoustic wave scattering problems (2010) (0)
$E_8$ Bundles and Rigidity (2013) (0)
Remarks on the Chern classes of Calabi-Yau moduli (2014) (0)
Soliton hierarchies constructed from involutions (2010) (0)
A Donaldson type functional on a holomorphic Finsler vector bundle (2016) (0)
D G ] 1 1 Se p 20 07 The hyperbolic geometric flow on Riemann surfaces (2009) (0)
A pr 2 01 8 CHERN FORMS OF HOLOMORPHIC FINSLER VECTOR BUNDLES AND SOME APPLICATIONS (2018) (0)
Se p 20 05 ON THE ASYMPTOTIC EXPANSION OF BERGMAN KERNEL (0)
Levi-Civita Ricci-flat metrics on compact complex manifolds (2019) (0)
Boltje-Maisch resolutions of Specht modules (2013) (0)
Rational curves on Hermitian manifolds (2014) (0)
A Basis of the q-Schur Module A (2013) (0)
Cohomology algebras in symplectic, Kähler and algebraic geometry (2010) (0)
EFFECTIVE RECURSION FORMULAE FOR COMPUTING INTERSECTION NUMBERS (2008) (0)
Harmonic 2-forms and positively curved 4-manifolds (2019) (0)
ON THE CARTAN FORMULA AND ITS APPLICATIONS (2012) (0)
Adiabatic Limits and Foliations Kefeng Liu and Weiping Zhang (2001) (0)
Open Problems (2019) (0)
Bases of $q$-Schur Module $\mathcal{A}^{\lambda}$ (2014) (0)
Bases of q-Schur Module A λ (2014) (0)
Higher Weil-Petersson Volumes and Tautological Constants (2007) (0)
Remarks on BCOV invariants and degenerations of Calabi-Yau manifolds (2018) (0)
Mirror Symmetry and Localizations (2006) (0)
Two new identities of intersection numbers on moduli spaces of curves (2006) (0)
Partition functions and box–spline (2010) (0)
3 1 M ar 2 00 4 K-theory associated to vertex operator algebras (2004) (0)
Good Geometry of the Moduli Spaces of Riemann Surfaces (2007) (0)
A geometric heat flow for vector fields (2014) (0)
Geometry of moduli spaces (2019) (0)
R T ] 2 0 M ay 2 01 3 A Basis of the q-Schur Module (2014) (0)
On a problem of Kuiper (2001) (0)
Quasi-isometry and deformations of Calabi–Yau manifolds (2014) (0)
Ju l 2 00 8 Time-Periodic Solutions of the Einstein ’ s Field Equations II (2008) (0)
A Brief Summary of My Researches (2002) (0)
Proceedings of the 4th International Congress of Chinese Mathematicians : Hangzhou 2007, December 17-22 (2008) (0)
Time-periodic universes (2008) (0)
On positive scalar curvature and moduli of curves (2015) (0)
Boundedness of the period maps and global Torelli theorem (2016) (0)
Torelli for some moduli spaces (2010) (0)
2 2 M ay 2 00 8 Time-Periodic Solutions of the Einstein ’ s Field Equations (2008) (0)
Affine geometry and Frobenius algebra (2021) (0)
Boundedness of the Images of Period Maps (2014) (0)
LOCALIZATION , HURWITZ NUMBERS AND THE WITTEN (2009) (0)
Congruence Skein Relations for Colored HOMFLY -PT Invariants (2022) (0)
Harmonic 2-forms and positively curved 4-manifolds (2020) (0)
Ja n 20 05 A FORMULA OF TWO-PARTITION HODGE INTEGRALS (2019) (0)
A pr 2 00 4 ON THE ASYMPTOTIC EXPANSION OF BERGMAN KERNEL (0)
Preface to Bogomolov special issue (2008) (0)
Intersection numbers on $\bar{\sM}_{g,n}$ and automorphisms of stable curves (2006) (0)
Applications of affine structures to Calabi–Yau moduli spaces (2016) (0)
Deformations of complex orbifolds and the period maps (2018) (0)
A note on modular forms and generalized anomaly cancellation formulas (2012) (0)
D G ] 2 0 A ug 2 01 8 GEODESIC-EINSTEIN METRICS AND NONLINEAR STABILITIES (2018) (0)
Shing-Tung Yau and Sixty Years of Calabi’s Conjecture (2013) (0)
2 0 A pr 2 00 4 K-theory associated to vertex operator algebras (2004) (0)

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