Edit Profile (opens in new tab) Yau, Shing-Tung Compute Distance To: Compute Author ID: yau.shing-tung Published as: Yau, Shing-Tung; Yau, S.-T.; Yau, Shing Tung; Yau, S. T.; Yau, Shingtung; Yau, Shing-tung; Yau, Sing-Tung more...less Further Spellings: 丘成桐 Homepage: http://doctoryau.com External Links: MacTutor · MGP · Wikidata · Google Scholar · Math-Net.Ru · dblp · GND · IdRef Awards: Fields Medal (1982) · Wolf Prize (2010) Documents Indexed: 564 Publications since 1970, including 14 Books 133 Contributions as Editor · 8 Further Contributions Biographic References: 21 Publications Co-Authors: 325 Co-Authors with 705 Joint Publications 8,274 Co-Co-Authors all top 5 Co-Authors 112 single-authored 45 Lian, Bong H. 43 Liu, Kefeng 37 Ji, Lizhen 30 Schoen, Richard Melvin 25 Jerison, David S. 25 Wang, Mu-Tao 24 Gu, Xianfeng 22 Cao, Huai-Dong 21 Chen, PoNing 19 Smoller, Joel Alan 18 Cheng, Shiu-Yuen 17 Chung, Fan 17 Lin, Yong 17 Stanley, Richard Peter 16 Finster, Felix 16 Grigor’yan, Alexander Asaturovich 15 Yang, Lo 14 Hosono, Shinobu 14 Jost, Jürgen 14 Li, Jun 14 Mazur, Barry 14 Schmid, Wilfried 14 Yau, Stephen Shing-Toung 14 Zeng, Wei 13 Li, Peter 13 Lin, Wen-Wei 12 Lui, Lok Ming 12 Luo, Feng 12 Mrowka, Tomasz S. 11 Sun, Xiaofeng 11 Tseng, Li-Sheng 10 Gu, Xianfeng David 10 Huang, An 9 Meeks, William Hamilton III 9 Muranov, Yuriĭ Vladimirovich 9 Yau, Horng-Tzer 9 Zaslow, Eric 8 Fu, Jixiang 8 Kamran, Niky 8 Kisin, Mark 8 Singer, Isadore Manuel 8 Wang, Yalin 8 Wang, Ye-Kai 8 Xie, Dan 8 Yueh, Mei-Heng 7 Bieri, Lydia 7 Gu, David Xianfeng 7 Klemm, Albrecht 7 Siu, Yum-Tong 7 Zheng, Fangyang 6 Lin, Hai 6 Liu, Chien-Hao 6 Lusztig, George 6 Nadis, Steve 6 Papadopoulos, Athanase 6 Seidel, Paul 6 Tian, Gang 6 Wu, Damin 5 Bourguignon, Jean-Pierre 5 Chan, Tony Fan-Cheong 5 Collins, Tristan Clifford 5 Dai, Junfei 5 Jaffe, Arthur Michael 5 Lu, Linyuan 5 Miller, Warner Allen 5 Oguiso, Keiji 5 Poon, Yat Sun 5 Sheshmani, Artan 5 Xu, Hao 4 Alsing, Paul M. 4 Becker, Melanie 4 Bott, Raoul Harry 4 Chen, Bingyi 4 Esole, Mboyo 4 Greene, Robert Everist 4 Hübsch, Tristan 4 Jin, Miao 4 Kang, Ming-Chang 4 Lawson, Herbert Blaine jun. 4 Leung, Naichung Conan 4 Li, Tiexiang 4 Lippner, Gábor 4 Liu, Chiu-Chu Melissa 4 Luo, Wei 4 Phong, Duong Hong 4 Roan, Shih-shyr 4 Shu, Chi-Wang 4 Theisen, Stefan J. 4 Uhlenbeck, Karen Keskulla 4 Wang, Juven 4 Zuo, Huaiqing 3 Alim, Murad 3 Au, Thomas Kwok-Keung 3 Bauer, Frank 3 Chruściel, Piotr Tadeusz 3 de Jong, Aise Johan 3 Gao, Peng 3 Greene, Brian R. 3 Gukov, Sergei 3 Haghighat, Babak ...and 307 more Co-Authors all top 5 Serials 46 Communications in Mathematical Physics 26 Advances in Theoretical and Mathematical Physics 25 Advanced Lectures in Mathematics (ALM) 24 Communications in Analysis and Geometry 19 Pure and Applied Mathematics Quarterly 18 ICCM Notices 17 Surveys in Differential Geometry 15 Journal of Differential Geometry 14 Communications in Information and Systems 14 AMS/IP Studies in Advanced Mathematics 13 Mathematische Annalen 12 Communications on Pure and Applied Mathematics 12 The Asian Journal of Mathematics 11 American Journal of Mathematics 11 Inventiones Mathematicae 10 Nuclear Physics. B 10 Mathematical Research Letters 8 Notices of the American Mathematical Society 7 Proceedings of the National Academy of Sciences of the United States of America 7 Annals of Mathematics. Second Series 6 Advances in Mathematics 6 Topology 5 Commentarii Mathematici Helvetici 5 Journal of Scientific Computing 5 Surveys in Differential Geometry. Supplement to the Journal of Differential Geometry 5 Communications in Number Theory and Physics 4 Classical and Quantum Gravity 4 Acta Mathematica 4 Journal of the American Mathematical Society 4 Science in China. Series A 4 Methods and Applications of Analysis 4 Journal of High Energy Physics 4 Proceedings of Symposia in Pure Mathematics 3 Journal of Mathematical Physics 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Mathematische Zeitschrift 3 Homology, Homotopy and Applications 3 Annales Henri Poincaré 3 SIAM Journal on Imaging Sciences 2 Modern Physics Letters A 2 International Journal of Modern Physics A 2 Physics Letters. B 2 Compositio Mathematica 2 Journal of Combinatorial Theory. Series A 2 Journal of Computational and Applied Mathematics 2 SIAM Journal on Control and Optimization 2 Computer Aided Geometric Design 2 Annals of Physics 2 Bulletin of the American Mathematical Society. New Series 2 Nuclear Physics. B. Proceedings Supplements 2 Journal of Algebraic Geometry 2 International Journal of Modern Physics D 2 Turkish Journal of Mathematics 2 Physical Review Letters 2 Conference Proceedings and Lecture Notes in Geometry and Topology 2 Surveys of Modern Mathematics 2 Geometry, Imaging and Computing 2 Harvard University Center of Mathematical Sciences and Applications Series in Mathematics (CSMA) 1 International Journal of Modern Physics B 1 Discrete Mathematics 1 Journal of Mathematical Analysis and Applications 1 Letters in Mathematical Physics 1 Physics Letters. A 1 Mathematics of Computation 1 Annales de l’Institut Fourier 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Applied Mathematics and Computation 1 Applied Mathematics and Optimization 1 Duke Mathematical Journal 1 Illinois Journal of Mathematics 1 Indiana University Mathematics Journal 1 Journal of Graph Theory 1 Journal für die Reine und Angewandte Mathematik 1 Manuscripta Mathematica 1 The Mathematics Student 1 Michigan Mathematical Journal 1 Numerische Mathematik 1 Pacific Journal of Mathematics 1 Proceedings of the American Mathematical Society 1 Proceedings of the London Mathematical Society. Third Series 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Tôhoku Mathematical Journal. Second Series 1 Topology and its Applications 1 Advances in Applied Mathematics 1 Annals of Global Analysis and Geometry 1 SIAM Journal on Matrix Analysis and Applications 1 Forum Mathematicum 1 CAD. Computer-Aided Design 1 Journal of the Ramanujan Mathematical Society 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 Random Structures & Algorithms 1 IMRN. International Mathematics Research Notices 1 Applied Mathematical Modelling 1 L’Enseignement Mathématique. 2e Série 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Acta Mathematica Sinica. New Series 1 SIAM Journal on Scientific Computing 1 Calculus of Variations and Partial Differential Equations 1 Combinatorics, Probability and Computing 1 Journal of Mathematical Sciences (New York) ...and 30 more Serials all top 5 Fields 333 Differential geometry (53-XX) 193 Algebraic geometry (14-XX) 153 Several complex variables and analytic spaces (32-XX) 136 General and overarching topics; collections (00-XX) 125 Quantum theory (81-XX) 112 Global analysis, analysis on manifolds (58-XX) 98 Relativity and gravitational theory (83-XX) 74 Partial differential equations (35-XX) 53 History and biography (01-XX) 53 Manifolds and cell complexes (57-XX) 42 Numerical analysis (65-XX) 41 Combinatorics (05-XX) 27 Functions of a complex variable (30-XX) 27 Computer science (68-XX) 26 Algebraic topology (55-XX) 25 Number theory (11-XX) 24 Calculus of variations and optimal control; optimization (49-XX) 18 Probability theory and stochastic processes (60-XX) 15 Convex and discrete geometry (52-XX) 13 Group theory and generalizations (20-XX) 13 Topological groups, Lie groups (22-XX) 9 Category theory; homological algebra (18-XX) 9 Special functions (33-XX) 9 Systems theory; control (93-XX) 8 Ordinary differential equations (34-XX) 7 Potential theory (31-XX) 7 Mechanics of particles and systems (70-XX) 6 Nonassociative rings and algebras (17-XX) 5 Geometry (51-XX) 5 Statistical mechanics, structure of matter (82-XX) 5 Biology and other natural sciences (92-XX) 5 Mathematics education (97-XX) 4 Commutative algebra (13-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Associative rings and algebras (16-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Difference and functional equations (39-XX) 4 Operator theory (47-XX) 4 Statistics (62-XX) 3 General topology (54-XX) 3 Information and communication theory, circuits (94-XX) 2 Field theory and polynomials (12-XX) 2 Real functions (26-XX) 2 Measure and integration (28-XX) 2 Abstract harmonic analysis (43-XX) 2 Functional analysis (46-XX) 2 Mechanics of deformable solids (74-XX) 2 Astronomy and astrophysics (85-XX) 1 \(K\)-theory (19-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 435 Publications have been cited 13,016 times in 8,562 Documents Cited by ▼ Year ▼ On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation. I. Zbl 0369.53059Yau, Shing-Tung 736 1978 On the parabolic kernel of the Schrödinger operator. Zbl 0611.58045Li, Peter; Yau, Shing Tung 424 1986 Harmonic functions on complete Riemannian manifolds. Zbl 0291.31002Yau, Shing-tung 403 1975 Lectures on differential geometry. Zbl 0830.53001Schoen, Richard; Yau, Shing-Tung 387 1994 Differential equations on Riemannian manifolds and their geometric applications. Zbl 0312.53031Cheng, S. Y.; Yau, Shing-Tung 382 1975 On the proof of the positive mass conjecture in general relativity. Zbl 0405.53045Schoen, Richard; Yau, Shing-Tung 350 1979 Some function-theoretic properties of complete Riemannian manifold and their applications to geometry. Zbl 0335.53041Yau, Shing-Tung 337 1976 Mirror symmetry is \(T\)-duality. Zbl 0896.14024Strominger, A.; Yau, S.-T.; Zaslow, E. 331 1996 On the existence of Hermitian-Yang-Mills connections in stable vector bundles. Zbl 0615.58045Uhlenbeck, K.; Yau, S. T. 272 1986 Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces. Zbl 0352.53021Cheng, Shiu-Yuen; Yau, Shing-Tung 259 1976 Calabi’s conjecture and some new results in algebraic geometry. Zbl 0355.32028Yau, Shing-Tung 216 1977 Conformally flat manifolds, Kleinian groups and scalar curvature. Zbl 0658.53038Schoen, Richard; Yau, Shing-Tung 212 1988 On the existence of a complete Kähler metric on non-compact complex manifolds and the regularity of Fefferman’s equation. Zbl 0506.53031Cheng, Shiu-Yuen; Yau, Shing-Tung 192 1980 Hypersurfaces with constant scalar curvature. Zbl 0349.53041Cheng, Shiu-Yuen; Yau, Shing-Tung 190 1977 On the Schrödinger equation and the eigenvalue problem. Zbl 0554.35029Li, Peter; Yau, Shing-Tung 186 1983 A general Schwarz lemma for Kähler manifolds. Zbl 0424.53040Yau, Shing-Tung 171 1978 Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature. Zbl 0431.53051Schoen, Richard; Yau, Shing-Tung 169 1979 Proof of the positive mass theorem. II. Zbl 0494.53028Schoen, Richard; Yau, Shing-Tung 168 1981 A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces. Zbl 0503.53042Li, Peter; Yau, Shing-Tung 166 1982 On the structure of manifolds with positive scalar curvature. Zbl 0423.53032Schoen, Richard; Yau, Shing-Tung 155 1979 Submanifolds with constant mean curvature. I. Zbl 0304.53041Yau, Shing-Tung 131 1974 Curvature estimates for minimal hypersurfaces. Zbl 0323.53039Schoen, Richard; Simon, Leon; Yau, Shing-Tung 126 1975 Sasaki-Einstein manifolds and volume minimisation. Zbl 1161.53029Martelli, Dario; Sparks, James; Yau, Shing-Tung 123 2008 On the regularity of the Monge-Ampère equation \(\text{det}(\partial^2u/\partial x_1\partial x_j)=F(x,u)\). Zbl 0347.35019Cheng, Shiu-Yuen; Yau, Shing-Tung 117 1977 Complete affine hypersurfaces. I: The completeness of affine metrics. Zbl 0623.53002Cheng, Shiu-Yuen; Yau, Shing-Tung 115 1986 The geometric dual of \(a\)-maximisation for toric Sasaki-Einstein manifolds. Zbl 1190.53041Martelli, Dario; Sparks, James; Yau, Shing-Tung 111 2006 On the regularity of the solution of the \(n\)-dimensional Minkowski problem. Zbl 0363.53030Cheng, Shiu-Yuen; Yau, Shing-Tung 108 1976 Compact Kähler manifolds of positive bisectional curvature. Zbl 0442.53056Siu, Yum-Tong; Yau, Shing-Tung 108 1980 Mirror symmetry, mirror map and applications to Calabi-Yau hypersurfaces. Zbl 0814.53056Hosono, S.; Klemm, A.; Theisen, S.; Yau, S.-T. 105 1995 Stringy cosmic strings and noncompact Calabi-Yau manifolds. Zbl 0744.53045Greene, B. R.; Shapere, A.; Vafa, C.; Yau, Shing-Tung 102 1990 Harmonic maps and the topology of stable hypersurfaces and manifolds with non-negative Ricci curvature. Zbl 0361.53040Schoen, Richard; Yau, Shing-Tung 97 1976 Calabi-Yau four-folds for \(M\)- and \(F\)-theory compactifications. Zbl 0920.14016Klemm, A.; Lian, B.; Roan, S.-S.; Yau, S.-T. 91 1998 Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature. Zbl 0521.53007Meeks, William H. III; Simon, Leon; Yau, Shing-Tung 91 1982 A lower bound for the heat kernel. Zbl 0481.35003Cheeger, Jeff; Yau, Shing-Tung 88 1981 Lectures on harmonic maps. Zbl 0886.53004Schoen, R.; Yau, S.-T. 87 1997 Mirror principle. I. Zbl 0953.14026Lian, Bong H.; Liu, Kefeng; Yau, Shing-Tung 85 1997 On the upper estimate of the heat kernel of a complete Riemannian manifold. Zbl 0484.53035Cheng, Siu Yuen; Li, Peter; Yau, Shing-Tung 84 1981 Local mirror symmetry: Calculations and interpretations. Zbl 0976.32012Chiang, T.-M.; Klemm, A.; Yau, S.-T.; Zaslow, E. 83 1999 Isoperimetric constants and the first eigenvalue of a compact Riemannian manifold. Zbl 0325.53039Yau, Shing-Tung 83 1975 Open problems in geometry. Zbl 0801.53001Yau, Shing Tung 78 1993 The existence of embedded minimal surfaces and the problem of uniqueness. Zbl 0479.49026Meeks, William H. III; Yau, Shing-Tung 78 1982 Ricci curvature and eigenvalue estimate on locally finite graphs. Zbl 1232.31003Lin, Yong; Yau, Shing-Tung 77 2010 The theory of superstring with flux on non-Kähler manifolds and the complex Monge-Ampère equation. Zbl 1141.53036Fu, Ji-Xiang; Yau, Shing-Tung 76 2008 Kähler-Einstein metrics on complex surfaces with \(C_ 1>0\). Zbl 0631.53052Tian, Gang; Yau, Shing Tung 75 1987 Topology of three dimensional manifolds and the embedding problems in minimal surface theory. Zbl 0458.57007Meeks, William H. III; Yau, Shing-Tung 75 1980 Eigenvalues of the Laplacian of compact Riemann surfaces and minimal submanifolds. Zbl 0446.58017Yang, Paul C.; Yau, Shing-Tung 73 1980 On univalent harmonic maps between surfaces. Zbl 0388.58005Schoen, Richard; Yau, Shing-Tung 70 1978 Complete Kähler manifolds with zero Ricci curvature. I. Zbl 0719.53041Tian, G.; Yau, Shing Tung 68 1990 Li-Yau inequality on graphs. Zbl 1323.35189Bauer, Frank; Horn, Paul; Lin, Yong; Lippner, Gabor; Mangoubi, Dan; Yau, Shing-Tung 68 2015 Complete Kähler manifolds with zero Ricci curvature. II. Zbl 0766.53053Tian, Gang; Yau, Shing Tung 64 1991 The classical Plateau problem and the topology of three-dimensional manifolds. The embedding of the solution given by Douglas-Morrey and an analytic proof of Dehn’s lemma. Zbl 0489.57002Meeks, William H. III; Yau, Shing-Tung 63 1982 Definition of center of mass for isolated physical systems and unique foliations by stable spheres with constant mean curvature. Zbl 0858.53071Huisken, Gerhard; Yau, Shing-Tung 62 1996 Small resolutions of SU(5)-models in F-theory. Zbl 1447.81171Esole, Mboyo; Yau, Shing-Tung 61 2013 Ricci curvature of graphs. Zbl 1237.05204Lin, Yong; Lu, Linyuan; Yau, Shing-Tung 60 2011 On the heat kernel of a complete Riemannian manifold. Zbl 0405.35025Yau, Shing-Tung 59 1978 Canonical metrics on the moduli space of Riemann surfaces. I. Zbl 1078.30038Liu, Kefeng; Sun, Xiaofeng; Yau, Shing-Tung 59 2004 Obstructions to the existence of Sasaki-Einstein metrics. Zbl 1149.53026Gauntlett, Jerome P.; Martelli, Dario; Sparks, James; Yau, Shing-Tung 54 2007 Connectedness of the boundary in the AdS/CFT correspondence. Zbl 0978.53085Witten, Edward; Yau, S.-T. 54 1999 Compact manifolds of nonpositive curvature. Zbl 0266.53035Lawson, H. Blaine jun.; Yau, Shing-Tung 54 1972 Problem section of the seminar in differential geometry at Tokyo. Zbl 0479.53001Yau, Shing-Tung 54 1982 Seminar on differential geometry. Zbl 0471.00020 53 1982 On the curvature of compact Hermitian manifolds. Zbl 0299.53039Yau, Shing-Tung 53 1974 An estimate of the gap of the first two eigenvalues in the Schrödinger operator. Zbl 0603.35070Singer, I. M.; Wong, Bun; Yau, Shing-Tung; Yau, Stephen S.-T. 53 1985 Compact group actions and the topology of manifolds with non-positive curvature. Zbl 0424.58012Schoen, Richard; Yau, Shing-Tung 52 1979 Special Lagrangians, stable bundles and mean curvature flow. Zbl 1115.53054Thomas, R. P.; Yau, S.-T. 51 2002 The existence of supersymmetric string theory with torsion. Zbl 1102.53052Li, Jun; Yau, Shingtung 50 2005 Submanifolds with constant mean curvature. II. Zbl 0304.53042Yau, Shing-Tung 49 1975 Decay of solutions of the wave equation in the Kerr geometry. Zbl 1194.83015Finster, F.; Kamran, N.; Smoller, J.; Yau, S.-T. 49 2006 BPS states, string duality, and nodal curves on \(K3\). Zbl 0964.81521Yau, Shing-Tung; Zaslow, Eric 48 1996 A nonlinear elliptic system for maps from Hermitian to Riemannian manifolds and rigidity theorems in Hermitian geometry. Zbl 0806.53064Jost, Jürgen; Yau, Shing-Tung 44 1993 Positivity of quasilocal mass. Zbl 1267.83028Liu, Chiu-Chu Melissa; Yau, Shing-Tung 44 2003 Isometric embeddings into the Minkowski space and new quasi-local mass. Zbl 1195.53039Wang, Mu-Tao; Yau, Shing-Tung 42 2009 Anomaly cancellation and smooth non-Kähler solutions in heterotic string theory. Zbl 1192.81312Becker, Katrin; Becker, Melanie; Fu, Ji-Xiang; Tseng, Li-Sheng; Yau, Shing-Tung 41 2006 The existence of a black hole due to condensation of matter. Zbl 0541.53054Schoen, Richard; Yau, Shing-Tung 41 1983 Upper bound for the first eigenvalue of algebraic submanifolds. Zbl 0814.53040Bourguignon, Jean-Pierre; Li, Peter; Yau, Shing Tung 39 1994 The Poincaré-Lelong equation on complete Kähler manifolds. Zbl 0531.32007Mok, Ngaiming; Siu, Yum-Tong; Yau, Shing-Tung 39 1981 Canonical metrics on the moduli space of Riemann surfaces. II. Zbl 1086.32011Liu, Kefeng; Sun, Xiaofeng; Yau, Shing-Tung 39 2005 Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces. Zbl 1020.32508Hosono, S.; Klemm, A.; Theisen, S.; Yau, S.-T. 38 1995 Heat equations on minimal submanifolds and their applications. Zbl 0575.53038Cheng, Shiu-Yuen; Li, Peter; Yau, Shing-Tung 38 1984 The energy and the linear momentum of space-times in general relativity. Zbl 0934.83031Schoen, Richard; Yau, Shing Tung 37 1981 Discrete Green’s functions. Zbl 0963.65120Chung, Fan; Yau, S.-T. 37 2000 Nonlinear analysis in geometry. Zbl 0631.53002Yau, Shing Tung 35 1987 Smooth static solutions of the Einstein/Yang-Mills equations. Zbl 0755.53061Smoller, Joel A.; Wassermann, Arthur G.; Yau, S.-T.; McLeod, J. B. 35 1991 Balanced metrics on non-Kähler Calabi-Yau threefolds. Zbl 1264.32020Fu, Jixiang; Li, Jun; Yau, Shing-Tung 35 2012 A note on our previous paper: On the existence of Hermitian Yang-Mills connections in stable vector bundles. Zbl 0678.58041Uhlenbeck, K.; Yau, S. T. 35 1989 Taming symplectic forms and the Calabi-Yau equation. Zbl 1153.53054Tosatti, Valentino; Weinkove, Ben; Yau, Shing-Tung 34 2008 Logarithmic Harnack inequalities. Zbl 0880.58026Chung, F. R. K.; Yau, S.-T. 34 1996 The equivariant Dehn’s lemma and loop theorem. Zbl 0469.57005Meeks, William H. III; Yau, Shing-Tung 34 1981 Cohomology and Hodge theory on symplectic manifolds. I. Zbl 1275.53079Tseng, Li-Sheng; Yau, Shing-Tung 34 2012 From special Lagrangian to Hermitian-Yang-Mills via Fourier-Mukai transform. Zbl 1033.53044Leung, Naichung Conan; Yau, Shing-Tung; Zaslow, Eric 33 2000 Arithmetic properties of mirror map and quantum coupling. Zbl 0867.14017Lian, Bong H.; Yau, Shing-Tung 31 1996 Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces. Zbl 0908.32008Hosono, S.; Klemm, A.; Theisen, S.; Yau, S. T. 30 1995 Essays on mirror manifolds. Zbl 0816.00010 30 1992 GKZ-generalized hypergeometric systems in mirror symmetry of Calabi-Yau hypersurfaces. Zbl 0870.14028Hosono, S.; Lian, B. H.; Yau, S.-T. 30 1996 Graph homotopy and Graham homotopy. Zbl 0990.05120Chen, Beifang; Yau, Shing-Tung; Yeh, Yeong-Nan 29 2001 Complete Kähler manifolds with nonpositive curvature of faster than quadratic decay. Zbl 0358.32006Siu, Yum-Tong; Yau, Shing-Tung 29 1977 Three dimensional canonical singularity and five dimensional \(\mathcal{N} = 1 \) SCFT. Zbl 1380.81416Xie, Dan; Yau, Shing-Tung 29 2017 Existence of Kähler-Einstein metrics on complete Kähler manifolds and their applications to algebraic geometry. Zbl 0682.53064Tian, G.; Yau, S. T. 29 1987 Scalar curvature, non-abelian group actions, and the degree of symmetry of exotic spheres. Zbl 0297.57016Lawson, H. Blaine jun.; Yau, Shing-Tung 28 1974 A Monge-Ampère-type equation motivated by string theory. Zbl 1122.35145Fu, Jixiang; Yau, Shingtung 28 2007 Moment maps, nonlinear PDE and stability in mirror symmetry. I: Geodesics. Zbl 1469.58007Collins, Tristan C.; Yau, Shing-Tung 4 2021 The dynamical model for COVID-19 with asymptotic analysis and numerical implementations. Zbl 1481.92147Liu, Jijun; Wang, Liyan; Zhang, Qiang; Yau, Shing-Tung 3 2021 Supertranslation invariance of angular momentum. Zbl 1489.83004Chen, Po-Ning; Wang, Mu-Tao; Wang, Ye-Kai; Yau, Shing-Tung 1 2021 Weil-Petersson geometry on the space of Bridgeland stability conditions. Zbl 1464.32037Fan, Yu-Wei; Kanazawa, Atsushi; Yau, Shing-Tung 1 2021 Evolution of angular momentum and center of mass at null infinity. Zbl 1471.83004Chen, Po-Ning; Keller, Jordan; Wang, Mu-Tao; Wang, Ye-Kai; Yau, Shing-Tung 1 2021 Stable surfaces and free boundary marginally outer trapped surfaces. Zbl 1482.53014Alaee, Aghil; Lesourd, Martin; Yau, Shing-Tung 1 2021 On the sum of Ricci-curvatures for weighted graphs. Zbl 1486.53040Bai, Shuliang; Huang, An; Lu, Linyuan; Yau, Shing-Tung 1 2021 Convergent conformal energy minimization for the computation of disk parameterizations. Zbl 1482.65029Kuo, Yueh-Cheng; Lin, Wen-Wei; Yueh, Mei-Heng; Yau, Shing-Tung 1 2021 Evaluating quasi-local angular momentum and center-of-mass at null infinity. Zbl 07433589Keller, Jordan; Wang, Ye-Kai; Yau, Shing-Tung 1 2021 \((1,1)\) forms with specified Lagrangian phase: a priori estimates and algebraic obstructions. Zbl 1442.14124Collins, Tristan C.; Jacob, Adam; Yau, Shing-Tung 10 2020 Localized Donaldson-Thomas theory of surfaces. Zbl 1442.14175Gholampour, Amin; Sheshmani, Artan; Yau, Shing-Tung 10 2020 Existence of solutions to mean field equations on graphs. Zbl 1447.35338Huang, An; Lin, Yong; Yau, Shing-Tung 7 2020 Invariant metrics on negatively pinched complete Kähler manifolds. Zbl 07171893Wu, Damin; Yau, Shing-Tung 6 2020 Nested Hilbert schemes on surfaces: virtual fundamental class. Zbl 1437.14054Gholampour, Amin; Sheshmani, Artan; Yau, Shing-Tung 6 2020 Quasi-local energy with respect to de Sitter/anti-de Sitter reference. Zbl 1467.53020Chen, Po-Ning; Wang, Mu-Tao; Yau, Shing-Tung 3 2020 Computational conformal geometry behind modern technologies. Zbl 1464.53003Gu, Xianfeng; Luo, Feng; Yau, Shing-Tung 2 2020 Path complexes and their homologies. Zbl 1448.05171Grigor’yan, A. A.; Lin, Yong; Muranov, Yu. V.; Yau, Shing-Tung 1 2020 Optimized surface parameterizations with applications to Chinese virtual broadcasting. Zbl 07267851Yueh, Mei-Heng; Huang, Hsiao-Han; Li, Tiexiang; Lin, Wen-Wei; Yau, Shing-Tung 1 2020 \(K3\) surfaces from configurations of six lines in \(\mathbb{P}^2\) and mirror symmetry. I. Zbl 1457.14084Hosono, Shinobu; Lian, Bong H.; Takagi, Hiromichi; Yau, Shing-Tung 1 2020 A new efficient algorithm for volume-preserving parameterizations of genus-one 3-manifolds. Zbl 1457.65016Yueh, Mei-Heng; Li, Tiexiang; Lin, Wen-Wei; Yau, Shing-Tung 1 2020 Volume doubling, Poincaré inequality and Gaussian heat kernel estimate for non-negatively curved graphs. Zbl 1432.35213Horn, Paul; Lin, Yong; Liu, Shuang; Yau, Shing-Tung 10 2019 A novel stretch energy minimization algorithm for equiareal parameterizations. Zbl 1417.65112Yueh, Mei-Heng; Lin, Wen-Wei; Wu, Chin-Tien; Yau, Shing-Tung 7 2019 Li-Yau inequality for unbounded Laplacian on graphs. Zbl 1428.35651Gong, Chao; Lin, Yong; Liu, Shuang; Yau, Shing-Tung 7 2019 Poisson metrics on flat vector bundles over non-compact curves. Zbl 1422.53057Collins, Tristan C.; Jacob, Adam; Yau, Shing-Tung 6 2019 A geometric view of optimal transportation and generative model. Zbl 1430.49050Lei, Na; Su, Kehua; Cui, Li; Yau, Shing-Tung; Gu, Xianfeng David 5 2019 iSIRA: integrated shift-invert residual Arnoldi method for graph Laplacian matrices from big data. Zbl 1452.65067Huang, Wei-Qiang; Lin, Wen-Wei; Lu, Henry Horng-Shing; Yau, Shing-Tung 2 2019 Seiberg-Witten differential via primitive forms. Zbl 1412.81166Li, Si; Xie, Dan; Yau, Shing-Tung 1 2019 The shape of a life. One mathematician’s search for the universe’s hidden geometry. Zbl 1435.32001Yau, Shing-Tung; Nadis, Steve 1 2019 Quantum statistics and spacetime topology: quantum surgery formulas. Zbl 1427.81059Wang, Juven; Wen, Xiao-Gang; Yau, Shing-Tung 1 2019 The deformed Hermitian-Yang-Mills equation in geometry and physics. Zbl 1421.35300Collins, Tristan C.; Xie, Dan; Yau, Shing-Tung 10 2018 ADE string chains and mirror symmetry. Zbl 1384.81125Haghighat, Babak; Yan, Wenbin; Yau, Shing-Tung 9 2018 On the path homology theory of digraphs and Eilenberg-Steenrod axioms. Zbl 1391.05125Grigor’yan, Alexander; Jimenez, Rolando; Muranov, Yuri; Yau, Shing-Tung 7 2018 D-type fiber-base duality. Zbl 1398.83108Haghighat, Babak; Kim, Joonho; Yan, Wenbin; Yau, Shing-Tung 7 2018 Calabi-Yau volumes and reflexive polytopes. Zbl 1404.14050He, Yang-Hui; Seong, Rak-Kyeong; Yau, Shing-Tung 5 2018 Quasi-local energy with respect to a static spacetime. Zbl 1400.83003Chen, Po-Ning; Wang, Mu-Tao; Wang, Ye-Kai; Yau, Shing-Tung 4 2018 Complete Kähler-Einstein metrics under certain holomorphic covering and examples. (Métriques complètes de Kähler-Einstein sous certains revêtements holomorphes et exemples.) Zbl 1426.32012Wu, Damin; Yau, Shing-Tung 3 2018 Evaluating small sphere limit of the Wang-Yau quasi-local energy. Zbl 1390.83052Chen, Po-Ning; Wang, Mu-Tao; Yau, Shing-Tung 3 2018 Path homology theory of multigraphs and quivers. Zbl 1404.55010Grigor’yan, Alexander; Muranov, Yuri; Vershinin, Vladimir; Yau, Shing-Tung 3 2018 On topological approach to local theory of surfaces in Calabi–Yau threefolds. Zbl 1447.81184Gukov, Sergei; Liu, Chiu-Chu Melissa; Sheshmani, Artan; Yau, Shing-Tung 1 2018 Wang and Yau’s quasi-local energy for an extreme Kerr spacetime. Zbl 1386.83054Miller, Warner A.; Ray, Shannon; Wang, Mu-Tao; Yau, Shing-Tung 1 2018 Period integrals and tautological systems. Zbl 1410.32008Huang, An; Lian, Bong; Yau, Shing-Tung; Yu, Chenglong 1 2018 On the existence of Hermitian Yang-Mills connections in stable vector bundles. Zbl 1415.32019Uhlenbeck, Karen; Yau, Shing-Tung 1 2018 Three dimensional canonical singularity and five dimensional \(\mathcal{N} = 1 \) SCFT. Zbl 1380.81416Xie, Dan; Yau, Shing-Tung 29 2017 A special Lagrangian type equation for holomorphic line bundles. Zbl 1375.32045Jacob, Adam; Yau, Shing-Tung 22 2017 Sharp Davies-Gaffney-Grigor’yan lemma on graphs. Zbl 1476.58027Bauer, Frank; Hua, Bobo; Yau, Shing-Tung 12 2017 An efficient energy minimization for conformal parameterizations. Zbl 1380.65049Yueh, Mei-Heng; Lin, Wen-Wei; Wu, Chin-Tien; Yau, Shing-Tung 10 2017 Pretty good quantum state transfer in symmetric spin networks via magnetic field. Zbl 1382.81049Kempton, Mark; Lippner, Gabor; Yau, Shing-Tung 9 2017 Braiding statistics and link invariants of bosonic/fermionic topological quantum matter in 2+1 and 3+1 dimensions. Zbl 1370.81157Putrov, Pavel; Wang, Juven; Yau, Shing-Tung 8 2017 Calabi-Yau modular forms in limit: elliptic fibrations. Zbl 1421.14009Haghighat, Babak; Movasati, Hossein; Yau, Shing-Tung 6 2017 Homologies of digraphs and Künneth formulas. Zbl 1381.05062Grigor’yan, Alexander; Muranov, Yuri; Yau, Shing-Tung 6 2017 4d \(\mathcal{N} = 2\) SCFT and singularity theory. II: Complete intersection. Zbl 1366.81256Chen, Bingyi; Xie, Dan; Yau, Shing-Tung; Yau, Stephen S.-T.; Zuo, Huaiqing 5 2017 \(4d\; \mathcal{N} = 2\) SCFT from complete intersection singularity. Zbl 1384.81139Wang, Yifan; Xie, Dan; Yau, Stephen S.-T.; Yau, Shing-Tung 4 2017 Curvatures of moduli space of curves and applications. Zbl 1388.53077Liu, Kefeng; Sun, Xiaofeng; Yang, Xiaokui; Yau, Shing-Tung 4 2017 A strong Harnack inequality for graphs. Zbl 1378.05119Chung, Fan; Yau, Shing-Tung 3 2017 String-Math 2015. Proceedings of the conference, Tsinghua Sanya International Mathematics Forum in Sanya, China, December 31, 2015 – January 4, 2016. Zbl 1381.14004 2 2017 Quasi-local mass at the null infinity of the Vaidya spacetime. Zbl 1380.83078Chen, Po-Ning; Wang, Mu-Tao; Yau, Shing-Tung 2 2017 Nonexistence for complete Kähler-Einstein metrics on some noncompact manifolds. Zbl 1382.32017Gao, Peng; Yau, Shing-Tung; Zhou, Wubin 1 2017 The rest mass of an asymptotically anti-de Sitter spacetime. Zbl 1367.83010Chen, Po-Ning; Hung, Pei-Ken; Wang, Mu-Tao; Yau, Shing-Tung 1 2017 Singularities and gauge theory phases. II. Zbl 1428.81124Esole, Mboyo; Shao, Shu-Heng; Yau, Shing-Tung 24 2016 Negative holomorphic curvature and positive canonical bundle. Zbl 1357.53085Wu, Damin; Yau, Shing-Tung 24 2016 Variational principles for Minkowski type problems, discrete optimal transport, and discrete Monge-Ampère equations. Zbl 1339.49039Gu, Xianfeng; Luo, Feng; Sun, Jian; Yau, Shing-Tung 17 2016 A remark on our paper “negative holomorphic curvature and positive canonical bundle”. Zbl 1373.53100Wu, Damin; Yau, Shing-Tung 15 2016 Cohomology and Hodge theory on symplectic manifolds. III. Zbl 1353.53085Tsai, Chung-Jun; Tseng, Li-Sheng; Yau, Shing-Tung 8 2016 Airy equation for the topological string partition function in a scaling limit. Zbl 1338.81305Alim, Murad; Yau, Shing-Tung; Zhou, Jie 6 2016 Heterotic string compactification and new vector bundles. Zbl 1342.81450Lin, Hai; Wu, Baosen; Yau, Shing-Tung 6 2016 Gauss-Manin connection in disguise: Calabi-Yau threefolds. Zbl 1348.14103Alim, Murad; Movasati, Hossein; Scheidegger, Emanuel; Yau, Shing-Tung 5 2016 Quasilocal angular momentum and center of mass in general relativity. Zbl 1355.83004Chen, Po-Ning; Wang, Mu-Tao; Yau, Shing-Tung 4 2016 On the validity of the definition of angular momentum in general relativity. Zbl 1335.83006Chen, Po-Ning; Huang, Lan-Hsuan; Wang, Mu-Tao; Yau, Shing-Tung 4 2016 On a cohomology of digraphs and Hochschild cohomology. Zbl 1353.05056Grigor’yan, Alexander; Muranov, Yuri; Yau, Shing-Tung 4 2016 On complete constant scalar curvature Kähler metrics with Poincaré-Mok-Yau asymptotic property. Zbl 1345.53077Fu, Jixiang; Yau, Shing-Tung; Zhou, Wubin 3 2016 Semicontinuity of 4d \( \mathcal{N}=2 \) spectrum under renormalization group flow. Zbl 1388.81896Xie, Dan; Yau, Shing-Tung 2 2016 Chain integral solutions to tautological systems. Zbl 1364.14031Huang, An; Lian, Bong H.; Yau, Shing-Tung; Zhu, Xinwen 2 2016 Conserved quantities on asymptotically hyperbolic initial data sets. Zbl 1367.83011Chen, Po-Ning; Wang, Mu-Tao; Yau, Shing-Tung 2 2016 From Riemann and Kodaira to modern developments on complex manifolds. Zbl 1354.53004Yau, Shing-Tung 1 2016 Computational conformal geometry. Reprint of the 2008 hardback edition. Zbl 1339.65001 1 2016 Li-Yau inequality on graphs. Zbl 1323.35189Bauer, Frank; Horn, Paul; Lin, Yong; Lippner, Gabor; Mangoubi, Dan; Yau, Shing-Tung 68 2015 \(D_5\) elliptic fibrations: non-Kodaira fibers and new orientifold limits of F-theory. Zbl 1333.81329Esole, Mboyo; Fullwood, James; Yau, Shing-Tung 21 2015 Singularities and gauge theory phases. Zbl 1428.81123Esole, Mboyo; Shao, Shu-Heng; Yau, Shing-Tung 21 2015 Invariant solutions to the Strominger system on complex Lie groups and their quotients. Zbl 1319.32022Fei, Teng; Yau, Shing-Tung 19 2015 Spanning trees and random walks on weighted graphs. Zbl 1307.05207Chang, Xiao; Xu, Hao; Yau, Shing-Tung 12 2015 Davies-Gaffney-Grigor’yan Lemma on graphs. Zbl 1342.58013Bauer, Frank; Hua, Bobo; Yau, Shing-Tung 10 2015 Non-Kähler SYZ mirror symmetry. Zbl 1328.53108Lau, Siu-Cheong; Tseng, Li-Sheng; Yau, Shing-Tung 10 2015 Conserved quantities in general relativity: from the quasi-local level to spatial infinity. Zbl 1319.83011Chen, Po-Ning; Wang, Mu-Tao; Yau, Shing-Tung 10 2015 Cohomology of digraphs and (undirected) graphs. Zbl 1329.05132Grigor’yan, Alexander; Lin, Yong; Muranov, Yuri; Yau, Shing-Tung 8 2015 Convergence of an iterative algorithm for Teichmüller maps via harmonic energy optimization. Zbl 1320.30040Lui, Lok Ming; Gu, Xianfeng; Yau, Shing-Tung 8 2015 Time-dependent Hermite-Galerkin spectral method and its applications. Zbl 1410.65398Luo, Xue; Yau, Shing-Tung; Yau, Stephen S.-T. 3 2015 Gravitational waves and their memory in general relativity. Zbl 1339.83004Bieri, Lydia; Garfinkle, David; Yau, Shing-Tung 3 2015 On the pseudonorm project of birational classification of algebraic varieties. Zbl 1322.14033Yau, Shing-Tung 3 2015 Extremal bundles on Calabi-Yau threefolds. Zbl 1328.14068Gao, Peng; He, Yang-Hui; Yau, Shing-Tung 2 2015 Complete cscK metrics on the local models of the conifold transition. Zbl 1316.32017Fu, Jixiang; Yau, Shing-Tung; Zhou, Wubin 2 2015 Adiabatic isometric mapping algorithm for embedding 2-surfaces in Euclidean 3-space. Zbl 1329.83049Ray, Shannon; Miller, Warner A.; Alsing, Paul M.; Yau, Shing-Tung 1 2015 Accelerating black holes, spin-\(\frac{3}{2}\) fields and \(C\)-metric. Zbl 1310.83021Lin, Hai; Saifullah, K.; Yau, Shing-Tung 1 2015 Harnack inequalities for graphs with non-negative Ricci curvature. Zbl 1309.05117Chung, Fan; Lin, Yong; Yau, S.-T. 25 2014 Teichmüller mapping (T-map) and its applications to landmark matching registration. (Teichmuller mapping (T-map) and its applications to landmark matching registration.) Zbl 1296.65028Lui, Lok Ming; Lam, Ka Chun; Yau, Shing-Tung; Gu, Xianfeng 25 2014 Special polynomial rings, quasi modular forms and duality of topological strings. Zbl 1314.14081Alim, Murad; Scheidegger, Emanuel; Yau, Shing-Tung; Zhou, Jie 24 2014 Homotopy theory for digraphs. Zbl 1312.05063Grigor’yan, Alexander; Lin, Yong; Muranov, Yuri; Yau, Shing-Tung 14 2014 Ricci-flat graphs with girth at least five. Zbl 1308.05038Lin, Yong; Lu, Linyuan; Yau, S.-T. 12 2014 Generalized cohomologies and supersymmetry. Zbl 1288.81125Tseng, Li-Sheng; Yau, Shing-Tung 12 2014 Graphs associated with simplicial complexes. Zbl 1297.05269Grigor’yan, A.; Muranov, Yu. V.; Yau, Shing-Tung 9 2014 A novel symmetric skew-Hamiltonian isotropic Lanczos algorithm for spectral conformal parameterizations. 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