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丘成桐综述文章选集: 附评论 (第 I 卷) ![]()
几何分析是近几十年来非常重要的学科,比如拓扑中的著名庞加莱猜想的解决实际上利用了几何分析的思想和方法。丘成桐教授是现代几何分析的奠基人之一,也是积极的参与者。在伟大的数学家当中,很少有像丘先生那样花费很多时间去撰写大量的综述文章。 《丘成桐综述文章选集(附评论第Ⅰ、Ⅱ卷)》收集了丘成桐教授2013年前所有的综述文章及丘先生总结的微分几何未解决问题的论述。更重要的是,丘先生对每篇文章都在当今意义下作出了评论并指出该论题的最新进展,对未解决问题也作了系统的分析及这些问题的最新总结。本书主编还特邀请了多位相关领域专家对丘先生工作及相关领域最新结果作出了评论。可以说这两卷著作就是近代几何分析发展的缩影,每一位对几何分析感兴趣的学生和专家都可以从中获益。 本书是其中的第Ⅰ卷。
丘成桐先生是当代最伟大的数学大师之一,著名科学家,哈佛大学数学系系主任、讲座教授,清华大学数学科学中心主任。丘先生1949年生于广东,22岁获博士学位。他获得了菲尔兹奖、沃尔夫奖、克莱福特奖、美国国家科学奖等国际顶级大奖,是美、俄、中、意四国科学院院士。他解决了“卡拉比猜想”、广义相对论中的“正质量猜想”、超弦理论中的“镜对称猜想”等众多世界难题。他是几何分析学科奠基人,他领导的团队为解决“庞加莱猜想”作出了重要贡献。他在中国大陆、香港、台湾创办了五大数学研究机构,领导举办了世界华人数学家大会,创办了丘成桐中学数学奖、丘成桐数学英才班、丘成桐大学生数学竞赛、新世界数学奖、晨兴数学奖,在国内出版了《微分几何》、《调和映照讲义》等专著,创办了《数学与人文》、《数学与数学人》科普丛书,为中国的人才培养、科学研究、学术交流以及中国数学界与海外科研学术合作作出了巨大贡献,荣获国务院颁发的中华人民共和国国际科技合作奖。
Preface
Shing-Tung Yau Shing-Tung Yau, His Mathematics and Writings Lizhen Ji Commentary on Metriques de Kahler-Einstein Sur les Varietes Ouvertes Metriques de Kahler-Einstein Sur les Varietes Ouvertes Shing-Tung Yau Commentary on The Classical Plateau Problem and the Topology of 3-manifolds The Classical Plateau Problem and the Topology of 3-manifolds William H. Meeks III, Shing-Tung Yau Commentary on Geometric Bounds on the Low Eigenvalues of a Compact Surface Geometric Bounds on the Low Eigenvalues of a Compact Surface Preface Shing-Tung Yau Shing-Tung Yau, His Mathematics and Writings Lizhen Ji Commentary on Metriques de Kahler-Einstein Sur les Varietes Ouvertes Metriques de Kahler-Einstein Sur les Varietes Ouvertes Shing-Tung Yau Commentary on The Classical Plateau Problem and the Topology of 3-manifolds The Classical Plateau Problem and the Topology of 3-manifolds William H. Meeks III, Shing-Tung Yau Commentary on Geometric Bounds on the Low Eigenvalues of a Compact Surface Geometric Bounds on the Low Eigenvalues of a Compact Surface R. Schoen, S. Wolpert, and S. T. Yau Commentary on Estimates of Eigenvalues of a Compact Riemannian Manifold Estimates of Eigenvalues of a Compact Riemannian Manifold Peter Li and Shing-Tung Yau Commentary on The Total Mass and the Topology of an Asymptotically Flat Space-time The Total Mass and the Topology of an Asymptotically Flat Space-time Shing-Tung Yau Commentary on The Role of Partial Differential Equations in Differential Geometry The Role of Partial Differential Equations in Differential Geometry Shing-Tung Yau Commentary on The Real Monge-Ampere Equation and Affine Flat Structures The Real Monge-Ampere Equation and Affine Flat Structures Shiu- Yuen Cheng and Shing-Tung Yau Commentary on Survey on Partial Differential Equations in Differential Geometry Survey on Partial Differential Equations in Differential Geometry Shing-Tung Yau Commentary on Problem Section Problem Section (With Commentary) Shing-Tung Yau Commentary on A Survey on Kahler-Einstein Metrics A Survey on Kahler-Einstein Metrics Shing-Tung Yau Commentary on Compact Three Dimensional Kahler Manifolds with Zero Ricci Curvature Compact Three Dimensional Kahler Manifolds with Zero Ricci Curvature Shing-Tung Yau Commentary on Inequality Between Chern Numbers of Singular Kahler Surfaces and Characterization of Orbit Space of Discrete Group of SU(2, 1) Inequality Between Chern Numbers of Singular Kahler Surfaces and Characterization of Orbit Space of Discrete Group of SU(2, 1) Shiu- Yuen Cheng and Shing-Tung Yau Commentary on On Ricci Flat 3-fold On Ricci Flat 3-fold Shi-Shyr Roan and Shing-Tung Yau Commentary on Some Recent Developments in General Relativity Some Recent Developments in General Relativity Shing-Tung Yau Commentary on Nonlinear Analysis in Geometry Nonlinear Analysis in Geometry Shing-Tung Yau Commentary on Three-Dimensional Algebraic Manifolds with C1 = O and X = -6 Three-Dimensional Algebraic Manifolds with C1 = O and X = -6 Gang Tian and Shing-Tung Yau Commentary on Uniformization of Geometric Structures Uniformization of Geometric Structures Shing-Tung Yau Commentary on Some Remarks on the Quasi-local Mass Some Remarks on the Quasi-local Mass D. Christodoulou and S.-T. Yau Commentary on A Review of Complex Differential Geometry A Review of Complex Differential Geometry Shing-Tung Yau Commentary on Open Problems in Geometry Open Problems in Geometry Shing-Tung Yau Commentary on On the Geometry of Certain Superconformal Field Theory Paradigms (Towards a Quantum Algebraic Geometry) On the Geometry of Certain Superconformal Field Theory Paradigms (Towards a Quantum Algebraic Geometry) Tristan Hiibsch and Shing-Tung Yau Commentary on Upper Bound for the First Eigenvalue of Algebraic Submanifolds Upper Bound for the First Eigenvalue of Algebraic Submanifolds Jean-Pierre Bourguignon, Peter Li, and Shing-Tung Yau Commentary on Review on Kahler-Einstein Metrics in Algebraic Geometry Review on Kahler-Einstein Metrics in Algebraic Geometry Shing-Tung Yau Commentary on A Note on The Distribution of Critical Points of Eigenfunctions A Note on The Distribution of Critical Points of Eigenfunctions Shing-Tung Yau Commentary on Sobolev Inequality for Measure Space Sobolev Inequality for Measure Space Shing-Tung Yau Commentary on Einstein Manifolds with Zero Ricci Curvature Einstein Manifolds with Zero Ricci Curvature Shing-Tung Yau Commentary on Review of Geometry and Analysis Review of Geometry and Analysis Shing-Tung Yau Commentary on Geometry and Spacetime Geometry and Spacetime Shing-Tung Yau Commentary on Geometry Motivated by Physics Geometry Motivated by Physics Shing-Tung Yau Commentary on Complex Geometry: Its Brief History and Its Future Complex Geometry: Its Brief History and Its Future Shing-Tung Yau Commentary on Geometric Aspects of the Moduli Space of Riemann Surfaces Geometric Aspects of the Moduli Space of Riemann Surfaces Kefeng Liu, Xiaofeng Sun, and Shing-Tung Yau Commentary on Solution of Filtering Problem with Nonlinear Observations Solution of Filtering Problem with Nonlinear Observations Stephen S.-T. Yau and Shing-Tung Yau Commentary on The Proof of the Poincare Conjecture The Proof of the Poincare Conjecture Shing-Tung Yau
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