Shing–Tung Yau

Research interests

Publications

• Evolutionary dynamics on any population structure

  Nature · 2017 · 10.1038/nature21723

• Ricci curvature of graphs

  Tohoku Mathematical Journal · 2011 · 10.2748/tmj/1325886283

• The theory of superstring with flux on non-Kähler manifolds and the complex Monge-Ampère equation

  Journal of Differential Geometry · 2008 · 10.4310/jdg/1207834550

• Global Conformal Surface Parameterization

  · 2003

• Local mirror symmetry: Calculations and interpretations

  Advances in Theoretical and Mathematical Physics · 1999 · 10.4310/atmp.1999.v3.n3.a3

• Mirror principle III

  Asian Journal of Mathematics · 1999 · 10.4310/ajm.1999.v3.n4.a4

• Mirror Symmetry is T-Duality

  arXiv (Cornell University) · 1996 · 10.48550/arxiv.hep-th/9606040

• Stringy cosmic strings and noncompact Calabi-Yau manifolds

  Nuclear Physics B · 1990 · 10.1016/0550-3213(90)90248-c

• Conformally flat manifolds, Kleinian groups and scalar curvature

  Inventiones mathematicae · 1988 · 10.1007/bf01393992

• On the existence of hermitian-yang-mills connections in stable vector bundles

  Communications on Pure and Applied Mathematics · 1986 · https://doi.org/10.1002/cpa.3160390714

• Complete affine hypersurfaces. Part I. The completeness of affine metrics

  Communications on Pure and Applied Mathematics · 1986 · 10.1002/cpa.3160390606

• A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces

  Inventiones mathematicae · 1982 · 10.1007/bf01399507

• Embedded Minimal Surfaces, Exotic Spheres, and Manifolds with Positive Ricci Curvature

  Annals of Mathematics · 1982 · 10.2307/2007026

• On the Upper Estimate of the Heat Kernel of a Complete Riemannian Manifold

  American Journal of Mathematics · 1981 · 10.2307/2374257

• A lower bound for the heat kernel

  Communications on Pure and Applied Mathematics · 1981 · 10.1002/cpa.3160340404

• On the existence of a complete Kähler metric on non‐compact complex manifolds and the regularity of fefferman's equation

  Communications on Pure and Applied Mathematics · 1980 · 10.1002/cpa.3160330404

• Compact k�hler manifolds of positive bisectional curvature

  Inventiones mathematicae · 1980 · 10.1007/bf01390043

• Existence of Incompressible Minimal Surfaces and the Topology of Three Dimensional Manifolds with Non-Negative Scalar Curvature

  Annals of Mathematics · 1979 · https://doi.org/10.2307/1971247

• On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I

  Communications on Pure and Applied Mathematics · 1978 · https://doi.org/10.1002/cpa.3160310304

• A General Schwarz Lemma for Kahler Manifolds

  American Journal of Mathematics · 1978 · 10.2307/2373880

• On the regularity of the monge‐ampère equation det (∂ 2 u/∂x i ∂x j ) = f(x, u)

  Communications on Pure and Applied Mathematics · 1977 · 10.1002/cpa.3160300104

• Hypersurfaces with constant scalar curvature

  Mathematische Annalen · 1977 · 10.1007/bf01425237

• Calabi's conjecture and some new results in algebraic geometry

  Proceedings of the National Academy of Sciences · 1977 · https://doi.org/10.1073/pnas.74.5.1798

• On the regularity of the solution of the n ‐dimensional Minkowski problem

  Communications on Pure and Applied Mathematics · 1976 · 10.1002/cpa.3160290504

• Differential equations on riemannian manifolds and their geometric applications

  Communications on Pure and Applied Mathematics · 1975 · https://doi.org/10.1002/cpa.3160280303

Current projects

No projects listed.