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The Ricci Flow in Riemannian Geometry

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

  • Ben Andrews
  • Christopher Hopper

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

  • Ben Andrews
    • 1
  • Christopher Hopper
    • 2
  1. 1.Mathematics and its ApplicationsAustralian National UniversityCanberraAustralia
  2. 2.Mathematical InstituteUniversity of OxfordOxfordUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-16286-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-16285-5
  • Online ISBN 978-3-642-16286-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site