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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