Description
Springer The Ricci Flow in Riemannian Geometry A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem by Ben Andrews, Christopher Hopper
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 Boehm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem._x000D_ Table of contents :- _x000D_
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 Boehm and Wilking.- 14 Preserving Positive Isotropic Curvature.- 15 The Final Argument_x000D_