# zbMATH — the first resource for mathematics

## Cheng, Shiu-Yuen

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 Author ID: cheng.shiu-yuen Published as: Cheng, S. Y.; Cheng, Shiu Yuen; Cheng, Shiu-Yuen; Cheng, Shiu-yuen; Cheng, Siu Yuen Homepage: https://www.math.ust.hk/people/faculty/macheng/ External Links: MGP · Wikidata
 Documents Indexed: 32 Publications since 1975, including 5 Books
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#### Co-Authors

 7 single-authored 13 Yau, Shing-Tung 3 Ji, Lizhen 3 Li, Peter 2 Shu, Chi-Wang 2 Tysk, Johan 2 Xu, Hao 2 Yang, Lo 1 Chen, Chyouhwa 1 Deng, Mo 1 He, Ronglu 1 Ji, Jizhen 1 Kang, Ming-Chang 1 Liu, Kefeng 1 Lu, Qikeng 1 Oden, Kevin 1 Poon, Yat Sun 1 Redheffer, Raymond M. 1 Tam, Luen-Fai 1 Tang, Tao 1 Wan, Tom Yau-Heng 1 Wang, Liping 1 Xiao, Jie 1 Yang, Xiao-Kui 1 Yau, Shek-Chung 1 Yau, Stephen Shing-Toung 1 Yu, Chenglong 1 Zhu, Xiping
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#### Serials

 5 Communications on Pure and Applied Mathematics 2 American Journal of Mathematics 2 Commentarii Mathematici Helvetici 2 Proceedings of the American Mathematical Society 1 Rocky Mountain Journal of Mathematics 1 Journal of Differential Equations 1 Mathematische Annalen 1 Mathematische Zeitschrift 1 Pacific Journal of Mathematics 1 The Journal of Geometric Analysis 1 Communications in Analysis and Geometry 1 Annals of Mathematics. Second Series 1 Scientia Sinica 1 Contemporary Mathematics 1 Advanced Lectures in Mathematics (ALM) 1 Journal of Theoretical Biology
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#### Fields

 25 Differential geometry (53-XX) 14 Global analysis, analysis on manifolds (58-XX) 12 Partial differential equations (35-XX) 5 General and overarching topics; collections (00-XX) 3 Algebraic geometry (14-XX) 3 Manifolds and cell complexes (57-XX) 2 History and biography (01-XX) 2 Number theory (11-XX) 2 Group theory and generalizations (20-XX) 2 Potential theory (31-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Numerical analysis (65-XX) 1 Combinatorics (05-XX) 1 Nonassociative rings and algebras (17-XX) 1 Topological groups, Lie groups (22-XX) 1 Algebraic topology (55-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX) 1 Biology and other natural sciences (92-XX)

#### Citations contained in zbMATH

24 Publications have been cited 1,751 times in 1,583 Documents Cited by Year
Differential equations on Riemannian manifolds and their geometric applications. Zbl 0312.53031
Cheng, S. Y.; Yau, Shing-Tung
1975
Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces. Zbl 0352.53021
Cheng, Shiu-Yuen; Yau, Shing-Tung
1976
Eigenvalue comparison theorems and its geometric applications. Zbl 0329.53035
Cheng, Shiu-Yuen
1975
On the existence of a complete Kähler metric on non-compact complex manifolds and the regularity of Fefferman’s equation. Zbl 0506.53031
Cheng, Shiu-Yuen; Yau, Shing-Tung
1980
Hypersurfaces with constant scalar curvature. Zbl 0349.53041
Cheng, Shiu-Yuen; Yau, Shing-Tung
1977
Eigenfunctions and nodal sets. Zbl 0334.35022
Cheng, Shiu-Yuen
1976
On the regularity of the Monge-Ampère equation $$\text{det}(\partial^2u/\partial x_1\partial x_j)=F(x,u)$$. Zbl 0347.35019
Cheng, Shiu-Yuen; Yau, Shing-Tung
1977
Complete affine hypersurfaces. I: The completeness of affine metrics. Zbl 0623.53002
Cheng, Shiu-Yuen; Yau, Shing-Tung
1986
On the regularity of the solution of the $$n$$-dimensional Minkowski problem. Zbl 0363.53030
Cheng, Shiu-Yuen; Yau, Shing-Tung
1976
On the upper estimate of the heat kernel of a complete Riemannian manifold. Zbl 0484.53035
Cheng, Siu Yuen; Li, Peter; Yau, Shing-Tung
1981
Heat equations on minimal submanifolds and their applications. Zbl 0575.53038
Cheng, Shiu-Yuen; Li, Peter; Yau, Shing-Tung
1984
Heat kernel estimates and lower bound of eigenvalues. Zbl 0484.53034
Cheng, Shiu-Yuen; Li, Peter
1981
The real Monge-Ampère equation and affine flat structures. Zbl 0517.35020
Cheng, Shiu-Yuen; Yau, Shing-Tung
1982
Liouville theorem for harmonic maps. Zbl 0455.58009
Cheng, Shiu-Yuen
1980
On the Schwarz lemma for complete Kähler manifolds. Zbl 0432.53010
Chen, C. H.; Cheng, Shiu-yuen; Look, K. H.
1979
Isoperimetric inequalities and the gap between the first and second eigenvalues of an Euclidean domain. Zbl 0920.58054
Cheng, Shiu-Yuen; Oden, Kevin
1997
Harmonic maps with finite total energy. Zbl 0871.53034
Cheng, Shiu-Yuen; Tam, Luen-Fai; Wan, Tom Y.-H.
1996
The Dirichlet problem at infinity for nonpositively curved manifolds. Zbl 0782.58046
Cheng, Shiu-Yuen
1993
Schrödinger operators and index bounds for minimal submanifolds. Zbl 0818.53075
Cheng, Shiu-Yuen; Tysk, Johan
1994
An index characterization of the catenoid and index bounds for minimal surfaces in $$R^ 4$$. Zbl 0613.58030
Cheng, Shiu-Yuen; Tysk, Johan
1988
Inequality between Chern numbers of singular Kähler surfaces and characterization of orbit space of discrete group of SU(2,1). Zbl 0597.53052
Cheng, S. Y.; Yau, S. T.
1986
Eigenfunctions and eigenvalues of Laplacian. Zbl 0308.35076
Cheng, Shiu-Yuen
1975
A characterization of the 2-sphere by eigenfunctions. Zbl 0327.53030
Cheng, Shiu-Yuen
1976
On the Chern conjecture for minimal hypersurface with constant scalar curvatures in the spheres. Zbl 0907.53041
Cheng, Shiu-Yuen
1997
Isoperimetric inequalities and the gap between the first and second eigenvalues of an Euclidean domain. Zbl 0920.58054
Cheng, Shiu-Yuen; Oden, Kevin
1997
On the Chern conjecture for minimal hypersurface with constant scalar curvatures in the spheres. Zbl 0907.53041
Cheng, Shiu-Yuen
1997
Harmonic maps with finite total energy. Zbl 0871.53034
Cheng, Shiu-Yuen; Tam, Luen-Fai; Wan, Tom Y.-H.
1996
Schrödinger operators and index bounds for minimal submanifolds. Zbl 0818.53075
Cheng, Shiu-Yuen; Tysk, Johan
1994
The Dirichlet problem at infinity for nonpositively curved manifolds. Zbl 0782.58046
Cheng, Shiu-Yuen
1993
An index characterization of the catenoid and index bounds for minimal surfaces in $$R^ 4$$. Zbl 0613.58030
Cheng, Shiu-Yuen; Tysk, Johan
1988
Complete affine hypersurfaces. I: The completeness of affine metrics. Zbl 0623.53002
Cheng, Shiu-Yuen; Yau, Shing-Tung
1986
Inequality between Chern numbers of singular Kähler surfaces and characterization of orbit space of discrete group of SU(2,1). Zbl 0597.53052
Cheng, S. Y.; Yau, S. T.
1986
Heat equations on minimal submanifolds and their applications. Zbl 0575.53038
Cheng, Shiu-Yuen; Li, Peter; Yau, Shing-Tung
1984
The real Monge-Ampère equation and affine flat structures. Zbl 0517.35020
Cheng, Shiu-Yuen; Yau, Shing-Tung
1982
On the upper estimate of the heat kernel of a complete Riemannian manifold. Zbl 0484.53035
Cheng, Siu Yuen; Li, Peter; Yau, Shing-Tung
1981
Heat kernel estimates and lower bound of eigenvalues. Zbl 0484.53034
Cheng, Shiu-Yuen; Li, Peter
1981
On the existence of a complete Kähler metric on non-compact complex manifolds and the regularity of Fefferman’s equation. Zbl 0506.53031
Cheng, Shiu-Yuen; Yau, Shing-Tung
1980
Liouville theorem for harmonic maps. Zbl 0455.58009
Cheng, Shiu-Yuen
1980
On the Schwarz lemma for complete Kähler manifolds. Zbl 0432.53010
Chen, C. H.; Cheng, Shiu-yuen; Look, K. H.
1979
Hypersurfaces with constant scalar curvature. Zbl 0349.53041
Cheng, Shiu-Yuen; Yau, Shing-Tung
1977
On the regularity of the Monge-Ampère equation $$\text{det}(\partial^2u/\partial x_1\partial x_j)=F(x,u)$$. Zbl 0347.35019
Cheng, Shiu-Yuen; Yau, Shing-Tung
1977
Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces. Zbl 0352.53021
Cheng, Shiu-Yuen; Yau, Shing-Tung
1976
Eigenfunctions and nodal sets. Zbl 0334.35022
Cheng, Shiu-Yuen
1976
On the regularity of the solution of the $$n$$-dimensional Minkowski problem. Zbl 0363.53030
Cheng, Shiu-Yuen; Yau, Shing-Tung
1976
A characterization of the 2-sphere by eigenfunctions. Zbl 0327.53030
Cheng, Shiu-Yuen
1976
Differential equations on Riemannian manifolds and their geometric applications. Zbl 0312.53031
Cheng, S. Y.; Yau, Shing-Tung
1975
Eigenvalue comparison theorems and its geometric applications. Zbl 0329.53035
Cheng, Shiu-Yuen
1975
Eigenfunctions and eigenvalues of Laplacian. Zbl 0308.35076
Cheng, Shiu-Yuen
1975
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#### Cited by 1,457 Authors

 54 de Lima, Henrique F. 30 Velásquez, Marco Antonio Lázaro 26 Romero, Alfonso 24 Alías, Luis J. 21 Rubio, Rafael María 18 Rigoli, Marco 18 Yau, Shing-Tung 17 Dos Santos, Fábio Reis 16 Bao, Jiguang 12 Grigor’yan, Alexander Asaturovich 12 Li, Peter 12 Ma, Ruyun 12 Bessa, Gregório Pacelli 11 Aquino, Cicero Pedro 11 Li, Haizhong 11 Wei, Guoxin 11 Wu, Jiayong 10 Tam, Luen-Fai 10 Xia, Changyu 10 Xu, Hongwei 9 Aledo, Juan Ángel 9 Dai, Guowei 9 Hua, Bobo 9 Li, Jiayu 9 Sun, Yuhua 8 Colares, Antonio Gervásio 8 Donnelly, Harold 8 Huang, Yong 8 Jian, Huaiyu 8 Jiang, Renjin 8 Jost, Jürgen 8 Li, An-Min 8 Tian, Gang 8 Wang, Linfeng 8 Wang, Xu-Jia 8 Yin, Weiping 8 Zhang, Zhijun 7 Cheng, Qingming 7 Fernández, Isabel 7 Huang, Guangyue 7 Li, Haigang 7 Mari, Luciano 7 Milán, Francisco 7 Urbas, John Ivan Eugene 7 Wang, Jiaping 7 Wang, Qiaoling 7 Wei, Guofang 7 Xin, Yuanlong 7 Xu, Zhiyuan 7 Zhang, Shicheng 6 Caballero, Magdalena 6 Caminha, Antonio 6 Colding, Tobias Holck 6 Colesanti, Andrea 6 Fernandes de Lima, Henrique 6 Holopainen, Ilkka 6 Miquel, Vicente 6 Munteanu, Ovidiu 6 Ni, Lei 6 Oliveira, Arlandson Matheus Silva 6 Pelegrín, José A. S. 6 Salamanca, Juan Jesús 6 Setti, Alberto G. 6 Shu, Shichang 6 Souam, Rabah 6 Takimoto, Kazuhiro 6 Wang, An 6 Xu, Man 6 Zhang, Gaoyong 6 Zhang, Xi 5 Albujer, Alma L. 5 Alencar, Hilário 5 Chang, Shu-Cheng 5 Chou, Kai-Seng 5 Gálvez, Jose Antonio 5 Gomes, José Nazareno Vieira 5 Guan, Bo 5 Guan, Pengfei 5 Honda, Shouhei 5 Ivaki, Mohammad N. 5 Kasue, Atsushi 5 Kim, Kang-Tae 5 Kobayashi, Ryoichi 5 Li, YanYan 5 Lions, Pierre-Louis 5 Markvorsen, Steen 5 Mira, Pablo 5 Mok, Ngaiming 5 Montenegro, José Fábio Bezerra 5 Nadirashvili, Nikolai S. 5 Palmer, Vicente 5 Pigola, Stefano 5 Schoen, Richard Melvin 5 Thalmaier, Anton 5 Torres, Pedro José 5 Trudinger, Neil Sidney 5 Vrancken, Luc 5 Wigman, Igor 5 Xiang, Ni 5 Xu, Ruiwei ...and 1,357 more Authors
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#### Cited in 221 Serials

 77 The Journal of Geometric Analysis 70 Journal of Mathematical Analysis and Applications 62 Proceedings of the American Mathematical Society 59 Transactions of the American Mathematical Society 57 Advances in Mathematics 50 Journal of Functional Analysis 50 Mathematische Zeitschrift 48 Calculus of Variations and Partial Differential Equations 46 Differential Geometry and its Applications 43 Mathematische Annalen 40 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 37 Journal of Geometry and Physics 32 Journal of Differential Equations 30 Annals of Global Analysis and Geometry 29 Manuscripta Mathematica 27 Inventiones Mathematicae 25 Duke Mathematical Journal 25 Geometriae Dedicata 24 Communications in Mathematical Physics 22 Results in Mathematics 20 Annales de l’Institut Fourier 19 Tohoku Mathematical Journal. Second Series 17 Monatshefte für Mathematik 15 Potential Analysis 15 Acta Mathematica Sinica. English Series 14 International Journal of Mathematics 13 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 12 Bulletin of the Australian Mathematical Society 12 General Relativity and Gravitation 12 Acta Mathematica 12 Geometric and Functional Analysis. GAFA 11 Communications in Partial Differential Equations 10 Rocky Mountain Journal of Mathematics 10 Chinese Annals of Mathematics. Series B 10 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 10 Journal of the American Mathematical Society 9 Archive for Rational Mechanics and Analysis 9 Annali di Matematica Pura ed Applicata. Serie Quarta 9 Mathematische Nachrichten 9 Science in China. Series A 9 Journal de Mathématiques Pures et Appliquées. Neuvième Série 9 Bulletin of the Brazilian Mathematical Society. New Series 9 Mediterranean Journal of Mathematics 8 Israel Journal of Mathematics 8 Journal of Mathematical Physics 8 Archiv der Mathematik 8 Journal für die Reine und Angewandte Mathematik 8 Kodai Mathematical Journal 8 Osaka Journal of Mathematics 8 Revista Matemática Iberoamericana 8 Bulletin of the American Mathematical Society. New Series 8 Communications in Contemporary Mathematics 8 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 Mathematical Proceedings of the Cambridge Philosophical Society 7 Glasgow Mathematical Journal 7 Nagoya Mathematical Journal 7 Science China. Mathematics 6 Communications on Pure and Applied Mathematics 6 Mathematical Notes 6 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 6 Compositio Mathematica 6 Journal of Geometry 6 Journal of Soviet Mathematics 6 Pacific Journal of Mathematics 6 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 6 Annals of Mathematics. Second Series 6 Frontiers of Mathematics in China 5 Beiträge zur Algebra und Geometrie 5 Linear Algebra and its Applications 5 Acta Mathematica Sinica. New Series 5 Bulletin des Sciences Mathématiques 5 Discrete and Continuous Dynamical Systems 5 Geometry & Topology 5 Advanced Nonlinear Studies 5 Communications on Pure and Applied Analysis 4 Journal of the Mathematical Society of Japan 4 Annales Henri Poincaré 4 International Journal of Geometric Methods in Modern Physics 4 Boundary Value Problems 4 Analysis & PDE 4 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 3 Journal d’Analyse Mathématique 3 Letters in Mathematical Physics 3 Anais da Academia Brasileira de Ciências 3 The Annals of Probability 3 Czechoslovak Mathematical Journal 3 Proceedings of the Japan Academy. Series A 3 Acta Mathematica Hungarica 3 Stochastic Processes and their Applications 3 Applied Mathematics. Series B (English Edition) 3 Journal of Mathematical Sciences (New York) 3 St. Petersburg Mathematical Journal 3 Mathematical Physics, Analysis and Geometry 3 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 3 Milan Journal of Mathematics 3 Advances in Difference Equations 3 Nonlinear Analysis. Theory, Methods & Applications 2 Applicable Analysis 2 Journal of Statistical Physics 2 Mathematical Methods in the Applied Sciences ...and 121 more Serials
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#### Cited in 45 Fields

 968 Differential geometry (53-XX) 545 Partial differential equations (35-XX) 442 Global analysis, analysis on manifolds (58-XX) 167 Several complex variables and analytic spaces (32-XX) 60 Potential theory (31-XX) 60 Convex and discrete geometry (52-XX) 49 Probability theory and stochastic processes (60-XX) 48 Calculus of variations and optimal control; optimization (49-XX) 39 Relativity and gravitational theory (83-XX) 28 Functions of a complex variable (30-XX) 26 Ordinary differential equations (34-XX) 25 Operator theory (47-XX) 22 Algebraic geometry (14-XX) 19 Combinatorics (05-XX) 18 Manifolds and cell complexes (57-XX) 12 Numerical analysis (65-XX) 11 Quantum theory (81-XX) 10 Functional analysis (46-XX) 8 Number theory (11-XX) 8 Topological groups, Lie groups (22-XX) 8 Real functions (26-XX) 8 Statistical mechanics, structure of matter (82-XX) 7 Special functions (33-XX) 7 Dynamical systems and ergodic theory (37-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 Abstract harmonic analysis (43-XX) 5 Statistics (62-XX) 5 Fluid mechanics (76-XX) 5 Optics, electromagnetic theory (78-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Difference and functional equations (39-XX) 4 Mechanics of particles and systems (70-XX) 3 Measure and integration (28-XX) 3 Algebraic topology (55-XX) 3 Mechanics of deformable solids (74-XX) 3 Operations research, mathematical programming (90-XX) 2 History and biography (01-XX) 2 Group theory and generalizations (20-XX) 2 Approximations and expansions (41-XX) 2 Integral transforms, operational calculus (44-XX) 2 General topology (54-XX) 1 General and overarching topics; collections (00-XX) 1 Nonassociative rings and algebras (17-XX) 1 Geometry (51-XX) 1 Biology and other natural sciences (92-XX)

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