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Record Nr. |
UNISA996466514903316 |
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Autore |
Andrews Ben |
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Titolo |
The Ricci Flow in Riemannian Geometry [[electronic resource] ] : A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem / / by Ben Andrews, Christopher Hopper |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2011 |
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ISBN |
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Edizione |
[1st ed. 2011.] |
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Descrizione fisica |
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1 online resource (XVIII, 302 p. 13 illus., 2 illus. in color.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 2011 |
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Disciplina |
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Soggetti |
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Partial differential equations |
Differential geometry |
Global analysis (Mathematics) |
Manifolds (Mathematics) |
Partial Differential Equations |
Differential Geometry |
Global Analysis and Analysis on Manifolds |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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 Böhm and Wilking -- 14 Preserving Positive Isotropic Curvature -- 15 The Final Argument. |
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Sommario/riassunto |
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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 Böhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem. |
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