Shing‐Tung Yau

1. On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I
   1978/05/01 by Shing‐Tung Yau, Shing–Tung Yau · 41 citations
   Engineering · Mathematics · #Algebraic Geometry and Number Theory #Citation #Computer science #Curvature #Engineering #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Library science #Manifold (fluid mechanics) #Mathematics #Pure mathematics #Reproduction #Ricci curvature
2. On the existence of a complete Kähler metric on non‐compact complex manifolds and the regularity of fefferman's equation
   1980/07/01 by Shiu‐Yuen Cheng, Shing–Tung Yau, Shing‐Tung Yau · 16 citations
   Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory
3. Geometric Understanding of Deep Learning
   2018/05/26 by Na Lei, Lei, Na, Zhongxuan Luo +7 · 1 voice · 3 citations
   Computer Science · Engineering · Mathematics · #Artificial intelligence #Artificial neural network #Computer science #Deep learning #Embedding #Engineering #Gaussian Processes and Bayesian Inference #Generative Adversarial Networks and Image Synthesis #Machine learning #Manifold (fluid mechanics) #Nonlinear dimensionality reduction #Pattern recognition (psychology) #Topological and Geometric Data Analysis #cs.LG #stat.ML
4. Maximal Space-like Hypersurfaces in the Lorentz-Minkowski Spaces
   1976/11/01 by Shiu-Yuen Cheng, Shiu‐Yuen Cheng, Shing‐Tung Yau +1 · 12 citations
   Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Mathematics and Applications
5. Homologies of path complexes and digraphs
   2012/07/12 by Alexander Grigorʼyan, Alexander Grigor'yan, Grigor'yan, Alexander +8 · 18 citations
   Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT #math.CO
6. On the regularity of the solution of the n ‐dimensional Minkowski problem
   1976/09/01 by Shiu‐Yuen Cheng, Shing–Tung Yau, Shing‐Tung Yau · 6 citations
   Mathematics · #Geometric Analysis and Curvature Flows #Numerical methods in inverse problems #Point processes and geometric inequalities
7. A note on our previous paper: On the existence of Hermitian Yang–Mills connections in stable vector bundles
   1989/07/01 by K. Uhlenbeck, Karen Uhlenbeck, Shing‐Tung Yau +1 · 6 citations
   Biochemistry, Genetics and Molecular Biology · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Microtubule and mitosis dynamics
8. On the regularity of the monge‐ampère equation det (∂ 2 u/∂x i ∂x j ) = f(x, u)
   1977/01/01 by Shiu‐Yuen Cheng, Shing–Tung Yau, Shing‐Tung Yau · 5 citations
   Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Functional Equations Stability Results
9. Harmonic functions on complete riemannian manifolds
   1975/03/01 by Shing‐Tung Yau · 4 citations
   Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Curvature #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Mathematical analysis #Mathematics #Pure mathematics #Ricci curvature #Riemannian manifold #Subharmonic function
10. Discrete Green's Functions
    2000/07/01 by Fan Chung, Shing‐Tung Yau, S.-T. Yau · 3 citations
    Computer Science · Mathematics · #Applied mathematics #Computer science #Differential equation #Discrete Poisson equation #Discrete time and continuous time #Geology #Graph theory and applications #Green S #Green's function for the three-variable Laplace equation #Inverse Laplace transform #Laplace transform #Laplace's equation #Markov Chains and Monte Carlo Methods #Markov chain #Mathematical analysis #Mathematical optimization #Mathematics #Matrix Theory and Algorithms #Statistics #Type (biology)
11. Mirror Principle III
    1999/12/06 by Bong H. Lian, B. Lian, K. Liu +5 · 3 citations
    Mathematics · #Advanced Operator Algebra Research #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #math.AG #math.DG
12. Fourier-Mukai number of a K3 surface
    2002/02/02 by Shinobu Hosono, Bong H. Lian, Hosono, Shinobu +6 · 2 citations
    Mathematics · #11A41 #11R29 #14J28 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Geometric and Algebraic Topology #math.AG #msc:11A41 #msc:11R29 #msc:14J28
13. Kummer structures on a K3 surface - An old question of T. Shioda
    2002/02/09 by Shinobu Hosono, Bong H. Lian, Hosono, Shinobu +6 · 1 citation
    Mathematics · #14J28 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #math.AG #msc:14J28
14. Mode Collapse and Regularity of Optimal Transportation Maps
    2019/02/08 by Na Lei, Lei, Na, Yang Guo +12 · 1 citation
    Computer Science · Economics, Econometrics and Finance · Environmental Science · Mathematics · #FOS: Computer and information sciences #Hydrology and Drought Analysis #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Monetary Policy and Economic Impact #Statistical Methods and Inference #cs.LG #stat.ML
15. AE-OT-GAN: Training GANs from data specific latent distribution
    2020/01/11 by Dongsheng An, Yang Guo, An, Dongsheng +12 · 1 citation
    Computer Science · Engineering · #Advanced Image Processing Techniques #Computer Vision and Pattern Recognition (cs.CV) #Digital Media Forensic Detection #FOS: Computer and information sciences #FOS: Electrical engineering #Generative Adversarial Networks and Image Synthesis #Image and Video Processing (eess.IV) #cs.CV #eess.IV #electronic engineering #information engineering
16. Complete affine hypersurfaces. Part I. The completeness of affine metrics
    1986/11/01 by Shiu‐Yuen Cheng, Shing–Tung Yau, Shing‐Tung Yau · 3 citations
    Mathematics · #Analytic and geometric function theory #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities
17. Relationships between cycle spaces, gain graphs, graph coverings, fundamental groups, path homology, and graph curvature
    2017/10/03 by Mark Kempton, Kempton, Mark, Florentin Münch +5 · 1 citation
    Computer Science · Mathematics · Medicine · #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders #Topological and Geometric Data Analysis #math.CO
18. A lower bound for the heat kernel
    1981/07/01 by Jeff Cheeger, Shing–Tung Yau, Shing‐Tung Yau · 3 citations
    Mathematics · #Center (category theory) #Citation #Combinatorics #Computer science #Graph theory and applications #Heat kernel #Kernel (algebra) #Library science #Mathematical Approximation and Integration #Mathematical analysis #Mathematics #Numerical methods in inverse problems #Upper and lower bounds