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The Ricci Flow in Riemannian Geometry : A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem / by Ben Andrews, Christopher Hopper

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerLink Bücher | Lecture notes in mathematics ; 2011Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011Description: Online-Ressource (X, 276p. 13 illus., 2 illus. in color, digital)ISBN:
  • 9783642162862
Subject(s): Additional physical formats: 9783642162855 | Buchausg. u.d.T.: The Ricci flow in Riemannian geometry. Heidelberg : Springer, 2011. XVII, 296 SeitenDDC classification:
  • 516.362
  • 515.353
MSC: MSC: *53-02 | 53C44RVK: RVK: SI 850 | SK 370LOC classification:
  • QA370-380
DOI: DOI: 10.1007/978-3-642-16286-2Online resources: Summary: 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 ArgumentSummary: 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 theoremPPN: PPN: 1650613083Package identifier: Produktsigel: ZDB-2-LNM | ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS
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