The Ricci flow in Riemannian geometry : a complete proof of the differentiable 1/4-pinching sphere theorem
著者
書誌事項
The Ricci flow in Riemannian geometry : a complete proof of the differentiable 1/4-pinching sphere theorem
（Lecture notes in mathematics, 2011）
Springer, c2011
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注記
Includes bibliographical references (p. 287-292) and index
内容説明・目次
内容説明
This book focuses on Hamilton's Ricci flow, beginning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compactness theorems for Riemannian manifolds, and Perelman's noncollapsing results, and culminating in a detailed analysis of the evolution of curvature, where recent breakthroughs of Boehm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem.
目次
1 Introduction.- 2 Background Material.- 3 Harmonic Mappings.- 4 Evolution of the Curvature.- 5 Short-Time Existence.- 6 Uhlenbeck's Trick.- 7 The Weak Maximum Principle.- 8 Regularity and Long-Time Existence.- 9 The Compactness Theorem for Riemannian Manifolds.- 10 The F-Functional and Gradient Flows.- 11 The W-Functional and Local Noncollapsing.- 12 An Algebraic Identity for Curvature Operators.- 13 The Cone Construction of Boehm and Wilking.- 14 Preserving Positive Isotropic Curvature.- 15 The Final Argument
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