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丘成桐綜述文章選集: 附評(píng)論 (第 I 卷)
幾何分析是近幾十年來非常重要的學(xué)科,比如拓?fù)渲械闹嫾尤R猜想的解決實(shí)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(xué)家當(dāng)中,很少有像丘先生那樣花費(fèi)很多時(shí)間去撰寫大量的綜述文章。 《丘成桐綜述文章選集(附評(píng)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(duì)每篇文章都在當(dāng)今意義下作出了評(píng)論并指出該論題的最新進(jìn)展,對(duì)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(qǐng)了多位相關(guān)領(lǐng)域?qū)<覍?duì)丘先生工作及相關(guān)領(lǐng)域最新結(jié)果作出了評(píng)論。可以說這兩卷著作就是近代幾何分析發(fā)展的縮影,每一位對(duì)幾何分析感興趣的學(xué)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(dāng)代最偉大的數(shù)學(xué)大師之一,著名科學(xué)家,哈佛大學(xué)數(shù)學(xué)系系主任、講座教授,清華大學(xué)數(shù)學(xué)科學(xué)中心主任。丘先生1949年生于廣東,22歲獲博士學(xué)位。他獲得了菲爾茲獎(jiǎng)、沃爾夫獎(jiǎng)、克萊福特獎(jiǎng)、美國(guó)國(guó)家科學(xué)獎(jiǎng)等國(guó)際頂級(jí)大獎(jiǎng),是美、俄、中、意四國(guó)科學(xué)院院士。他解決了“卡拉比猜想”、廣義相對(duì)論中的“正質(zhì)量猜想”、超弦理論中的“鏡對(duì)稱猜想”等眾多世界難題。他是幾何分析學(xué)科奠基人,他領(lǐng)導(dǎo)的團(tuán)隊(duì)為解決“龐加萊猜想”作出了重要貢獻(xiàn)。他在中國(guó)大陸、香港、臺(tái)灣創(chuàng)辦了五大數(shù)學(xué)研究機(jī)構(gòu),領(lǐng)導(dǎo)舉辦了世界華人數(shù)學(xué)家大會(huì),創(chuàng)辦了丘成桐中學(xué)數(shù)學(xué)獎(jiǎng)、丘成桐數(shù)學(xué)英才班、丘成桐大學(xué)生數(shù)學(xué)競(jìng)賽、新世界數(shù)學(xué)獎(jiǎng)、晨興數(shù)學(xué)獎(jiǎng),在國(guó)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(xué)與人文》、《數(shù)學(xué)與數(shù)學(xué)人》科普叢書,為中國(guó)的人才培養(yǎng)、科學(xué)研究、學(xué)術(shù)交流以及中國(guó)數(shù)學(xué)界與海外科研學(xué)術(shù)合作作出了巨大貢獻(xiàn),榮獲國(guó)務(wù)院頒發(fā)的中華人民共和國(guó)國(guó)際科技合作獎(jiǎng)。
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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