Lecture Notes in Mathematics

The Ricci Flow in Riemannian Geometry

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

Authors: Andrews, Ben, Hopper, Christopher

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  • Offers a self contained presentation of the proof of the differentiable sphere theorem
  • Presents the geometry of vector bundles in a form suitable for geometric PDE
  • Provides a discussion of the history of the sphere theorem and of future challenges
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About this book

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.

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)

Table of contents (15 chapters)

Table of contents (15 chapters)
  • Introduction

    Pages 1-9

    Andrews, Ben (et al.)

  • Background Material

    Pages 11-47

    Andrews, Ben (et al.)

  • Harmonic Mappings

    Pages 49-62

    Andrews, Ben (et al.)

  • Evolution of the Curvature

    Pages 63-82

    Andrews, Ben (et al.)

  • Short-Time Existence

    Pages 83-95

    Andrews, Ben (et al.)

Buy this book

eBook $54.99
price for USA in USD
  • ISBN 978-3-642-16286-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-3-642-16285-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
The Ricci Flow in Riemannian Geometry
Book Subtitle
A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2011
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-16286-2
DOI
10.1007/978-3-642-16286-2
Softcover ISBN
978-3-642-16285-5
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XVIII, 302
Number of Illustrations
11 b/w illustrations, 2 illustrations in colour
Topics