00000cmm a22000004a 4500 UP-99796217611212584 Buklod 20241010120843.0 m go j cr |n |||auu|a 241010s2011 gw o j eng d 9783642162862 (eBook) (iLib)UPD-00215704394 DMLR eng rda eng DMLUC QA 377.3 A53 2011eb Andrews, Ben. author. The ricci flow in Riemannian geometry a complete proof of the differentiable 1/4-pinching sphere theorem [electronic resource] Ben Andrews, Christopher Hopper. Heidelberg, Germany Springer Berlin 2011. 1 online resource illustrations text rdacontent computer rdamedia online resource rdacarrier Lecture notes in mathematics 2011 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. IP-based subscription, access limited to within on-campus computer network. Access via Electronic Resources of the UPD University Library Website. 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 Ricci flow. Geometry Riemannian. Mathematics Global analysis. Evolution equations. Available for UP System via Springer Link. https://link.springer.com/book/10.1007/978-3-642-16286-2 FO UPD DMLR QA 377.3 A53 2011eb Electronic Resource