Shing–Tung Yau

1. Differential equations on riemannian manifolds and their geometric applications
   1975/05/01 by S. Y. Cheng, Sheng Yao Cheng, S. T. Yau +1 · 65 citations
   Mathematics · Computer Science · #advanced mathematical theories #Algebraic and Geometric Analysis #Advanced Mathematical Modeling in Engineering
2. A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces
   1982/06/01 by Peter Li, Shing-Tung Yau, Shing–Tung Yau · 54 citations
   Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Advanced Differential Equations and Dynamical Systems
3. Existence of Incompressible Minimal Surfaces and the Topology of Three Dimensional Manifolds with Non-Negative Scalar Curvature
   1979/07/01 by R. Schoen, Shing–Tung Yau, Shing-Tung Yau · 52 citations
   Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Geometry Research
4. Conformally flat manifolds, Kleinian groups and scalar curvature
   1988/02/01 by R. Schoen, S. -T. Yau, Shing–Tung Yau · 24 citations
   Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Geometry Research
5. Heat Equations on Minimal Submanifolds and Their Applications
   1984/10/01 by Shiu-Yuen Cheng, Shiu‐Yuen Cheng, Peter Li +2 · 13 citations
   Mathematics · Computer Science · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering
6. Isometric Embeddings into the Minkowski Space and New Quasi-Local Mass
   2009/02/26 by Mu-Tao Wang, Mu‐Tao Wang, Shing–Tung Yau +1 · 16 citations
   Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories
7. (1,1) forms with specified Lagrangian phase: A priori estimates and\n algebraic obstructions
   2015/08/08 by Tristan C. Collins, Collins, Tristan C., Adam Jacob +4 · 9 citations
   Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Waves and Solitons
8. Positive Scalar Curvature and Minimal Hypersurface Singularities
   2017/04/18 by Shing–Tung Yau, Schoen, Richard, Yau, Shing-Tung · 4 citations
   Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
9. Ollivier Ricci-flow on weighted graphs
   2020/10/05 by Shuliang Bai, Bai, Shuliang, Yong Lin +7 · 5 citations
   Mathematics · Physics and Astronomy · #53C21 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
10. A special Lagrangian type equation for holomorphic line bundles
    2014/11/27 by Adam Jacob, Jacob, Adam, Shing–Tung Yau +1 · 3 citations
    Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
11. On the Sum of Ricci-Curvatures for Weighted Graphs
    2020/01/06 by Shuliang Bai, Bai, Shuliang, An Huang +5 · 3 citations
    Mathematics · Medicine · #05C10 #Advanced Neuroimaging Techniques and Applications #Combinatorics (math.CO) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
12. On Upper Bounds in Dimension Gaps of CFT's
    2022/01/10 by Tristan C. Collins, Collins, Tristan C., Daniel L. Jafferis +7 · 3 citations
    Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #High Energy Physics - Theory (hep-th)
13. A free boundary Monge-Ampère equation and applications to complete Calabi-Yau metrics
    2024/02/15 by Tristan C. Collins, Collins, Tristan C., Freid Tong +3 · 6 citations
    Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
14. Positive Scalar Curvature on Noncompact Manifolds and the Liouville Theorem
    2020/09/26 by Martin Lesourd, Ryan Unger, Lesourd, Martin +3 · 2 citations
    Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Cosmology and Gravitation Theories #Advanced Differential Geometry Research
15. Stability of the tangent bundle through conifold transitions
    2021/02/22 by Tristan C. Collins, Sébastien Picard, Collins, Tristan C. +3 · 3 citations
    Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th)
16. Computing Conformal Structure of Surfaces
    2002/12/13 by Xianfeng Gu, Gu, Xianfeng, Shing–Tung Yau +2 · 1 citation
    Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #Computer Graphics and Visualization Techniques #F.2.2 #FOS: Computer and information sciences #G.2.m #Graphics (cs.GR) #I.3.5 #cs.CG #cs.GR
17. Affine Manifolds, SYZ Geometry, and the "Y" Vertex
    2004/05/04 by John Loftin, Loftin, John, Shing–Tung Yau +3 · 1 citation
    Mathematics · #14J32 #81T30 #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #High Energy Physics - Theory (hep-th)
18. A degeneration formula of Gromov-Witten invariants with respect to a curve class for degenerations from blow-ups
    2004/08/11 by Chien-Hao Liu, Chien‐Hao Liu, Shing-Tung Yau +3 · 1 citation
    Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #hep-th #math.AG #msc:14N35 #msc:81T30
19. D-branes and Azumaya noncommutative geometry: From Polchinski to Grothendieck
    2010/03/05 by Chien‐Hao Liu, Shing–Tung Yau, Liu, Chien-Hao +1 · 4 citations
    Mathematics · Physics and Astronomy · #14A22 #53C38 #81T30 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
20. Existence of Supersymmetric Hermitian Metrics with Torsion on Non-Kaehler Manifolds
    2005/09/02 by Ji-Xiang Fu, Jixiang Fu, Fu, Ji-Xiang +3 · 2 citations
    Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #hep-th
21. On the Holonomic Rank Problem
    2013/02/18 by Spencer Bloch, An Huang, Bloch, Spencer +7 · 2 citations
    Mathematics · #14D07 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)
22. Stability for Line Bundles and Deformed Hermitian-Yang-Mills Equation on Some Elliptic Surfaces
    2023/06/09 by Tristan C. Collins, Jason Lo, Collins, Tristan C. +5 · 2 citations
    Mathematics · #Geometry and complex manifolds #Advanced Mathematical Physics Problems #Algebraic Geometry and Number Theory
23. Generalized Monge-Ampère functionals and related variational problems
    2023/06/02 by Freid Tong, Shing–Tung Yau, Tong, Freid +1 · 2 citations
    Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations
24. Futaki Invariants and Reflexive Polygons
    2024/10/24 by Jiakang Bao, Bao, Jiakang, Eugene Choi +7 · 1 voice · 3 citations
    Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
25. Discrete Morse Theory on Digraphs
    2021/02/21 by Yong Lin, Lin, Yong, Chong Wang +3 · 2 citations
    Computer Science · Mathematics · Medicine · #Topological and Geometric Data Analysis #Homotopy and Cohomology in Algebraic Topology #Advanced Neuroimaging Techniques and Applications
26. The deformed Hermitian-Yang-Mills equation in geometry and physics
    2017/12/04 by Tristan C. Collins, Collins, Tristan C., Xie Dan +3 · 1 citation
    Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons
27. Li-Yau inequality for unbounded Laplacian on graphs
    2018/01/18 by Chao Gong, Gong, Chao, Yong Lin +5 · 2 citations
    Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations
28. On exterior calculus and curvature in piecewise-flat manifolds
    2012/12/05 by Jonathan McDonald, Warner A. Miller, McDonald, Jonathan R. +9 · 1 citation
    Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Algebraic and Geometric Analysis #Relativity and Gravitational Theory
29. Rigid Schubert classes in partial flag varieties
    2024/01/21 by Liu Yuxiang, Liu, Yuxiang, Artan Sheshmani +3 · 1 citation
    Mathematics · Physics and Astronomy · #14M15 #14M17 #32M10 #51M35 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #FOS: Mathematics #Nonlinear Waves and Solitons
30. K stability and stability of chiral ring
    2016/06/29 by Tristan C. Collins, Dan Xie, Collins, Tristan C. +3 · 1 citation
    Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th)
31. A Neural Symbolic Model for Space Physics
    2025/03/11 by Jie Ying, Ying, Jie, Haowei Lin +17 · 2 citations
    Computer Science · Neuroscience · #Neural Networks and Applications #Cognitive Science and Education Research #Computational Physics and Python Applications
32. Multi-rigidity of Schubert classes in partial flag varieties
    2024/10/29 by Liu Yuxiang, Artan Sheshmani, Liu, Yuxiang +3 · 1 citation
    Mathematics · #14M15 #14M17 #32M10 #51M35 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics