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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| Autore: |
Andrews Ben
|
| 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
|
| Pubblicazione: | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2011 |
| Edizione: | 1st ed. 2011. |
| Descrizione fisica: | 1 online resource (XVIII, 302 p. 13 illus., 2 illus. in color.) |
| Disciplina: | 516.3/62 |
| Soggetto topico: | Partial differential equations |
| Differential geometry | |
| Global analysis (Mathematics) | |
| Manifolds (Mathematics) | |
| Partial Differential Equations | |
| Differential Geometry | |
| Global Analysis and Analysis on Manifolds | |
| Persona (resp. second.): | 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.: | 996466514903316 |
| Lo trovi qui: | Univ. di Salerno |
| Opac: | Controlla la disponibilità qui |
Serie:
Lecture Notes in Mathematics, . 0075-8434 ; ; 2011