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＜E-Book＞
The Ricci Flow in Riemannian Geometry : A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem / by Ben Andrews, Christopher Hopper
(Lecture Notes in Mathematics. ISSN:16179692 ; 2011)

Edition	1st ed. 2011.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	2011
Size	XVIII, 302 p. 13 illus., 2 illus. in color : online resource
Authors	*Andrews, Ben author Hopper, Christopher author SpringerLink (Online service)
Subjects	LCSH:Differential equations LCSH:Geometry, Differential LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) FREE:Differential Equations FREE:Differential Geometry FREE:Global Analysis and Analysis on Manifolds
Notes	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 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 HTTP:URL=https://doi.org/10.1007/978-3-642-16286-2

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