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.

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...

Table of Contents:

• 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.