| Description |
1 online resource (xvii, 296 pages) : illustrations |
| Series |
Lecture notes in mathematics, 0075-8434 ; 2011 |
|
Lecture notes in mathematics (Springer-Verlag) ; 2011.
|
| Contents |
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 |
| Summary |
Annotation 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 |
| Analysis |
wiskunde |
|
mathematics |
|
differentiaalmeetkunde |
|
differential geometry |
|
partial differential equations |
|
Mathematics (General) |
|
Wiskunde (algemeen) |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
|
Print version record |
| Subject |
Ricci flow.
|
|
Geometry, Riemannian.
|
|
Geometría riemanniana
|
|
Geometry, Riemannian
|
|
Ricci flow
|
| Form |
Electronic book
|
| Author |
Hopper, Christopher.
|
| ISBN |
9783642162862 |
|
364216286X |
|
