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1、2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。《丘成桐综述文章选集（附评论 第1卷）》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。
《丘成桐综述文章选集（附评论 第1卷）》是其中的第Ⅰ卷。
- Front Matter
- Volume I
- Preface:Shing-Tung Yau
- Shing-Tung Yau, His Mathematics and Writings:Lizhen Ji
- Commentary on:M_etriques de Kahler-Einstein Sur les Vari_et_es Ouvertes
- M_etriques de Kahler-Einstein Sur les Vari_et_es 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 Di_erential Equations in Di_erential Geometry
- The Role of Partial Di_erential Equations in Di_erential Geometry:Shing-Tung Yau
- Commentary on:The Real Monge-Amp_ere Equation and A_ne Flat Structures
- The Real Monge-Amp_ere Equation and A_ne Flat Structures:Shiu-Yuen Cheng and Shing-Tung Yau
- Commentary on:Survey on Partial Di_erential Equations in Di_erential Geometry
- Survey on Partial Di_erential Equations in Di_erential 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
- Inequality Between Chern Numbers of Singular Kahler Surfaces and Characterization of Orbit Space of Discrete Group of SU(2
- 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
