The Ricci flow in Riemannian geometry : a complete proof of the differentiable 1/4-pinching sphere theorem / / by Ben Andrews, Christopher Hopper
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| Autore: |
Andrews Ben
|
| Titolo: |
The Ricci flow in Riemannian geometry : a complete proof of the differentiable 1/4-pinching sphere theorem / / by Ben Andrews, Christopher Hopper
|
| Pubblicazione: | Heidelberg, : Springer-Verlag Berlin Heidelberg, 2010 |
| Edizione: | 1st ed. 2011. |
| Descrizione fisica: | 1 online resource (XVIII, 302 p. 13 illus., 2 illus. in color.) |
| Disciplina: | 516.3/62 |
| Soggetto topico: | Ricci flow |
| Geometry, Riemannian | |
| Differentiable dynamical systems | |
| Differential equations, Partial | |
| Global differential geometry | |
| Altri autori: |
HopperChristopher
|
| Note generali: | Bibliographic Level Mode of Issuance: Monograph |
| Nota di bibliografia: | Includes bibliographical references and index. |
| Nota di contenuto: | 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. |
| Sommario/riassunto: | 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. |
| Titolo autorizzato: | The Ricci flow in Riemannian geometry |
| ISBN: | 3-642-16286-X |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910484396803321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Lecture notes in mathematics (Springer-Verlag) ; ; 2011.