幾何分析是近幾十年來非常重要的學科,比如拓撲中的著名龐加萊猜想的解決實際上利用了幾何分析的思想和方法。丘成桐教授是現(xiàn)代幾何分析的奠基人之一,也是積極的參與者。在偉大的數(shù)學家當中,很少有像丘先生那樣花費很多時間去撰寫大量的綜述文章。 《丘成桐綜述文章選集(附評論第Ⅰ、Ⅱ卷)》收集了丘成桐教授2013年前所有的綜述文章及丘先生總結(jié)的微分幾何未解決問題的論述。更重要的是,丘先生對每篇文章都在當今意義下作出了評論并指出該論題的最新進展,對未解決問題也作了系統(tǒng)的分析及這些問題的最新總結(jié)。本書主編還特邀請了多位相關(guān)領(lǐng)域?qū)<覍η鹣壬ぷ骷跋嚓P(guān)領(lǐng)域最新結(jié)果作出了評論?梢哉f這兩卷著作就是近代幾何分析發(fā)展的縮影,每一位對幾何分析感興趣的學生和專家都可以從中獲益。 本書是其中的第Ⅰ卷。
丘成桐先生是當代最偉大的數(shù)學大師之一,著名科學家,哈佛大學數(shù)學系系主任、講座教授,清華大學數(shù)學科學中心主任。丘先生1949年生于廣東,22歲獲博士學位。他獲得了菲爾茲獎、沃爾夫獎、克萊福特獎、美國國家科學獎等國際頂級大獎,是美、俄、中、意四國科學院院士。他解決了“卡拉比猜想”、廣義相對論中的“正質(zhì)量猜想”、超弦理論中的“鏡對稱猜想”等眾多世界難題。他是幾何分析學科奠基人,他領(lǐng)導(dǎo)的團隊為解決“龐加萊猜想”作出了重要貢獻。他在中國大陸、香港、臺灣創(chuàng)辦了五大數(shù)學研究機構(gòu),領(lǐng)導(dǎo)舉辦了世界華人數(shù)學家大會,創(chuàng)辦了丘成桐中學數(shù)學獎、丘成桐數(shù)學英才班、丘成桐大學生數(shù)學競賽、新世界數(shù)學獎、晨興數(shù)學獎,在國內(nèi)出版了《微分幾何》、《調(diào)和映照講義》等專著,創(chuàng)辦了《數(shù)學與人文》、《數(shù)學與數(shù)學人》科普叢書,為中國的人才培養(yǎng)、科學研究、學術(shù)交流以及中國數(shù)學界與海外科研學術(shù)合作作出了巨大貢獻,榮獲國務(wù)院頒發(fā)的中華人民共和國國際科技合作獎。
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