The Ricci Flow in Riemannian Geometry A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem /

• Main Authors: Andrews, Ben (Author), Hopper, Christopher (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
• Series: Lecture Notes in Mathematics, 2011
• Subjects: Mathematics.; Global analysis (Mathematics).; Manifolds (Mathematics).; Partial differential equations.; Differential geometry.; Partial Differential Equations.; Differential Geometry.; Global Analysis and Analysis on Manifolds.
• Physical Description: XVIII, 302 p. 13 illus., 2 illus. in color. online resource.
• ISBN: 9783642162862
• ISSN: 0075-8434 ;

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.