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Lectures on the Ricci Flow

✍ Scribed by Peter Topping

Publisher
Cambridge University Press
Year
2006
Tongue
English
Leaves
122
Series
Graduate Studies in Mathematics, 325
Category
Library
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✦ Synopsis

An introduction to Ricci flow suitable for graduate students and research mathematicians.

✦ Table of Contents

Contents
Preface
1. Introduction
2. Riemannian geometry background
3. The maximum principle
4. Comments on existence theory for parabolic PDE
5. Existence theory for the Ricci flow
6. Ricci flow as a gradient flow
7. Compactness of Riemannian manifolds and flows
8. Perelman’s W entropy functional
9. Curvature pinching and preserved curvature properties under Ricci flow
10. Three-manifolds with positive Ricci curvature, and beyond
Appendix A. Connected sum
References
Index

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