Advertisement

© 2011

The Ricci Flow in Riemannian Geometry

A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem

  • A self contained presentation of the proof of the differentiable sphere theorem

  • A presentation of the geometry of vector bundles in a form suitable for geometric PDE

  • A discussion of the history of the sphere theorem and of future challenges

Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 2011)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Ben Andrews, Christopher Hopper
    Pages 1-9
  3. Ben Andrews, Christopher Hopper
    Pages 11-47
  4. Ben Andrews, Christopher Hopper
    Pages 49-62
  5. Ben Andrews, Christopher Hopper
    Pages 63-82
  6. Ben Andrews, Christopher Hopper
    Pages 83-95
  7. Ben Andrews, Christopher Hopper
    Pages 97-113
  8. Ben Andrews, Christopher Hopper
    Pages 115-135
  9. Ben Andrews, Christopher Hopper
    Pages 137-143
  10. Ben Andrews, Christopher Hopper
    Pages 145-159
  11. Ben Andrews, Christopher Hopper
    Pages 161-171
  12. Ben Andrews, Christopher Hopper
    Pages 173-191
  13. Ben Andrews, Christopher Hopper
    Pages 193-221
  14. Ben Andrews, Christopher Hopper
    Pages 223-233
  15. Ben Andrews, Christopher Hopper
    Pages 235-258
  16. Ben Andrews, Christopher Hopper
    Pages 259-269
  17. Back Matter
    Pages 287-296

About this book

Introduction

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.

Keywords

35-XX, 53-XX, 58-XX Ricci flow Riemannian geometry Sphere theorem

Authors and affiliations

  1. 1.Mathematics and its ApplicationsAustralian National UniversityCanberraAustralia
  2. 2.Mathematical InstituteUniversity of OxfordOxfordUnited Kingdom

Bibliographic information

Industry Sectors
Aerospace
Energy, Utilities & Environment
Finance, Business & Banking

Reviews

From the reviews:

“The book is dedicated almost entirely to the analysis of the Ricci flow, viewed first as a heat type equation hence its consequences, and later from the more recent developments due to Perelman’s monotonicity formulas and the blow-up analysis of the flow which was made thus possible. … is very enjoyable for specialists and non-specialists (of curvature flows) alike.” (Alina Stancu, Zentralblatt MATH, Vol. 1214, 2011)