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

Format:

Book

Author/Creator:

Andrews, Ben, author.

Hopper, Christopher, author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 2011.

Lecture Notes in Mathematics, 0075-8434 ; 2011

Language:

English

Subjects (All):

Differential equations, Partial.

Global differential geometry.

Global analysis (Mathematics).

Partial Differential Equations.

Differential Geometry.

Global Analysis and Analysis on Manifolds.

Local Subjects:

Partial Differential Equations.

Differential Geometry.

Global Analysis and Analysis on Manifolds.

Physical Description:

1 online resource (XVIII, 302 pages 13 illustrations, 2 illustrations in color).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.

System Details:

text file PDF

Summary:

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.

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.

Other Format:

Printed edition:

ISBN:

9783642162862

Access Restriction:

Restricted for use by site license.