Paul C. Yang | Academic Influence

Paul C. Yang's AcademicInfluence.com Rankings

Paul C. Yang

Mathematics

#707

World Rank

#1293

Historical Rank

#307

USA Rank

Measure Theory

#2400

World Rank

#2870

Historical Rank

#682

USA Rank

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Mathematics

Paul C. Yang's Degrees

PhD Mathematics University of California, Berkeley
Bachelors Mathematics National Taiwan University

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Why Is Paul C. Yang Influential?

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According to Wikipedia, Paul C. Yang is a Taiwanese-American mathematician specializing in differential geometry, partial differential equations and CR manifolds. He is best known for his work in Conformal geometry for his study of extremal metrics and his research on scalar curvature and Q-curvature. In CR Geometry he is known for his work on the CR embedding problem, the CR Paneitz operator and for introducing the Q' curvature in CR Geometry.

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Paul C. Yang'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

Prescribing Gaussian curvature on S2 (1987) (347)
Conformal deformation of metrics on $S^2$ (1988) (320)
Eigenvalues of the laplacian of compact Riemann surfaces and minimal submanifolds (1980) (293)
An equation of Monge-Ampère type in conformal geometry, and four-manifolds of positive Ricci curvature (2002) (266)
Extremal metrics of zeta function determinants on 4-manifolds (1995) (249)
The scalar curvature equation on 2- and 3-spheres (1993) (249)
A perturbation result in prescribing scalar curvature on $S^n$ (1991) (205)
On uniqueness of solutions of $n$-th order differential equations in conformal geometry (1997) (172)
Minimal surfaces in pseudohermitian geometry (2004) (143)
An a priori estimate for a fully nonlinear equation on four-manifolds (2002) (143)
A regularity theory of biharmonic maps (1999) (134)
Estimates and extremals for zeta function determinants on four-manifolds (1992) (131)
A conformally invariant sphere theorem in four dimensions (2003) (122)
The inequality of Moser and Trudinger and applications to conformal geometry (2003) (87)
Existence and uniqueness for P-area minimizers in the Heisenberg group (2006) (80)
Local boundary regularity of holomorphic mappings (1980) (77)
Compactification of a class of conformally flat 4-manifold (2000) (72)
Regularity of a fourth order nonlinear PDE with critical exponent (1999) (59)
Embeddability for Three-Dimensional Cauchy-Riemann Manifolds and CR Yamabe Invariants (2010) (58)
On the Chern-Gauss-Bonnet integral for conformal metrics on R4 (2000) (58)
Classification of singular radial solutions to the σk Yamabe equation on annular domains (2005) (57)
A perturbation result for prescribing mean curvature (1998) (57)
Isospectral conformal metrics on 3-manifolds (1990) (57)
A Paneitz-type operator for CR pluriharmonic functions (2013) (55)
On a class of locally conformally flat manifolds (2004) (54)
Isospectral sets of conformally equivalent metrics (1989) (52)
Q‐Curvature on a Class of Manifolds with Dimension at Least 5 (2014) (51)
Regularity of C1 smooth surfaces with prescribed p-mean curvature in the Heisenberg group (2007) (51)
Regularity of harmonic maps (1999) (45)
Sign of Green's function of Paneitz operators and the Q curvature (2014) (43)
A Positive Mass Theorem in Three Dimensional Cauchy–Riemann Geometry (2013) (42)
Entire Solutions of a Fully Nonlinear (2013) (39)
Conformal invariants associated to a measure. (2006) (38)
What is Q-Curvature? (2008) (38)
Lectures on the fourth order Q curvature equation (2015) (36)
A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group (2010) (35)
Compactness of isospectral conformal metrics onS3 (1989) (34)
Non-linear Partial Differential Equations in Conformai Geometry* (2002) (34)
Principal curvature estimates for the convex level sets of semilinearelliptic equations (2010) (34)
Isoperimetric inequalities & volume comparison theorems on cr manifolds (2009) (33)
On a Conformal Gap and Finiteness Theorem for a Class of Four-Manifolds (2005) (32)
Automorphisms of Tube Domains and Spherical Hypersurfaces (1985) (30)
Remarks on prescribing Gauss curvature (1993) (29)
CURVATURES OF COMPLEX SUBMANIFOLDS OF C n (2008) (29)
Regularity for n-harmonic maps (1996) (29)
Uniformization of spherical CR manifolds (2013) (29)
Q Curvature on a Class of 3‐Manifolds (2016) (28)
On Kähler manifolds with negative holomorphic bisectional curvature (1976) (27)
On the topology of conformally compact Einstein 4-manifolds (2003) (26)
Positivity of Paneitz operators (2001) (26)
Curvatures of complex submanifolds of $\mathbf{C}^n$ (1977) (25)
Automorphism of Tube Domains (1982) (24)
ON THE PANEITZ ENERGY ON STANDARD THREE SPHERE (2004) (23)
The Sobolev inequality for Paneitz operator on three manifolds (2004) (23)
Regularity forn-harmonic maps (1996) (23)
An overdetermined Neumann problem in the unit disk (1982) (22)
EMBEDDED THREE-DIMENSIONAL CR MANIFOLDS AND THE NON-NEGATIVITY OF PANEITZ OPERATORS (2012) (21)
Minimal surfaces in pseudohermitian geometry and the Bernstein problem in the Heisenberg group (2004) (20)
Umbilicity and characterization of Pansu spheres in the Heisenberg group (2014) (19)
On a fourth order equation in 3-D (2002) (18)
Some Progress in Conformal Geometry (2007) (16)
The CR Paneitz Operator and the Stability of CR Pluriharmonic Functions (2015) (15)
Compact Kähler-Einstein surfaces of nonpositive bisectional curvature (1981) (14)
Extremal metrics for the Q′-curvature in three dimensions (2015) (14)
On the prescribing σ2 curvature equation on S 4 (2011) (13)
Conformal energy in four dimension (2002) (13)
Partial differential equations related to the Gauss-Bonnet-Chern integrand on 4-manifolds (2002) (11)
On the prescribing σ2 curvature equation on $${\mathbb S^4}$$ (2011) (10)
A Remark on the Kernel of the CR Paneitz operator (2015) (10)
Multiple solutions and regularity of H-systems (1996) (10)
ON FINITENESS OF KLEINIAN GROUPS IN GENERAL DIMENSION (2003) (10)
Addendum to: “A perturbation result in prescribing scalar curvature on $S^n$” (1993) (9)
An integral formula for the $Q$-prime curvature in 3-dimensional CR geometry (2017) (8)
Paneitz operator for metrics near $S^3$ (2015) (8)
Geometric analysis and PDEs (2009) (8)
Conformal invariants associated to a measure: conformally covariant operators (2011) (8)
Kähler metrics on fibered manifolds (1977) (6)
A CONSTRUCTION OF M-HARMONIC MAPS OF SPHERES (1993) (6)
Isoperimetric inequality on CR-manifolds with nonnegative $Q'$-curvature (2016) (6)
Umbilic hypersurfaces of constant sigma-k curvature in the Heisenberg group (2015) (5)
CONFORMAL INVARIANTS ASSOCIATED TO A MEASURE , I : POINTWISE INVARIANTS (2007) (5)
FOURTH ORDER EQUATIONS IN CONFORMAL GEOMETRY by (2000) (5)
Paneitz operator for metrics near $$S^{3}$$S3 (2015) (5)
Pseudo-Hermitian Geometry in 3-D (2011) (4)
A Perturbation Approach for Paneitz Energy on Standard Three Sphere (2018) (4)
Some Remarks on the Geometry of a Class of Locally Conformally Flat Metrics (2020) (4)
Strong maximum principle for mean curvature operators on subRiemannian manifolds (2016) (4)
On the Sobolev quotient of three-dimensional CR manifolds (2019) (3)
Determinants and extremal metrics in conformal geometry (1997) (3)
Classification of singular radial solutions to the $\sigma_k$ Yamabe equation on annular domains (2004) (3)
The Lichnerowicz–Obata theorem for the Kohn Laplacian in three dimensions (2020) (3)
Scattering on singular Yamabe spaces (2021) (2)
Minimal Surfaces in CR Geometry (2009) (2)
A non-compact version of Plücker’s second equation (1980) (2)
Invariant surface area functionals and singular Yamabe problem in 3-dimensional CR geometry (2017) (2)
Monge-Ampere Type Equations and Applications (2003) (1)
Reduced power operations in motivic cohomology . Motivic cohomology with z/2-coefficients . A conformally invariant sphere theorem in four dimensions . Tameness on the boundary and Ahlfors' measure conjecture . Determinantal probability measures (2003) (1)
Spectral Invariants of Conformal Metrics (1991) (1)
On the Sobolev–Poincaré Inequality of CR-manifolds (2018) (1)
Quasiconformal flows on non-conformally flat spheres (2021) (1)
Optimal transportation on the hemisphere (2014) (1)
Isoperimetric domains in homogeneous three-manifolds and the isoperimetric constant of the Heisenberg group $\mathsf{H}^1$ (2015) (1)
ISOPERIMETRIC DOMAINS IN HOMOGENEOUS THREE-MANIFOLDS AND THE ISOPERIMETRIC CONSTANT OF THE HEISENBERG GROUP H (2015) (1)
Extremal metrics for the $Q^\prime$-curvature in three dimensions (2018) (1)
On the prescribing $\sigma_2$ curvature equation on $\mathbb S^4$ (2009) (1)
Extended Abstracts Fall 2013 : Geometrical Analysis; Type Theory, Homotopy Theory and Univalent Foundations (2015) (1)
Geometric Analysis (2020) (1)
ON PRESCRIBING GAUSS CURVATURE (2010) (0)
A ug 2 00 6 EXISTENCE AND UNIQUENESS FOR P-AREA MINIMIZERS IN THE HEISENBERG (2006) (0)
Abstracts 8 apr 2019 (2019) (0)
A CR invariant sphere theorem (2022) (0)
The Neumann problem on the Clifford torus in $\mathbb{S}^3$ (2023) (0)
PANEITZ OPERATOR FOR METRICS NEAR S (2017) (0)
Pseudo-Hermitian Geometry in 3D (2020) (0)
Strong maximum principle for mean curvature operators on subRiemannian manifolds (2018) (0)
CR geometry in 3-D (2017) (0)
Riemann-Roch Theorem for Strongly Pseudoconvex Manifolds of Dimension Three (1984) (0)
1 0 Ja n 20 06 EXISTENCE AND UNIQUENESS FOR P-AREA MINIMIZERS IN THE HEISENBERG (2009) (0)
The Jacobi Equation on a CR Manifold (2008) (0)
CR geometry in 3-D (2017) (0)
Geometric Analysis and PDEs: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 11-16, 2007 (2009) (0)
53–03 Historical (must Also Be Assigned at Least One Classification Number from Section 01) (0)
Extended abstracts fall 2013 (2015) (0)
pseudoconvex domain and Aut(D) = {f: D -- DI f a biholomorphic (2016) (0)
Some remarks on the symmetry and embedding of locally conformally flat metrics (2018) (0)

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