Lectures on the Ricci flow
Author(s)
Bibliographic Information
Lectures on the Ricci flow
（London Mathematical Society lecture note series, 325）
Cambridge University Press, 2006
- : pbk
Available at / 56 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: pbkS||LMS||32506053041
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
: pbk516.3/T6292080122885
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Note
Includes bibliographical references (p. 109-111) and index
Description and Table of Contents
Description
Hamilton's Ricci flow has attracted considerable attention since its introduction in 1982, owing partly to its promise in addressing the Poincare conjecture and Thurston's geometrization conjecture. This book gives a concise introduction to the subject with the hindsight of Perelman's breakthroughs from 2002/2003. After describing the basic properties of, and intuition behind the Ricci flow, core elements of the theory are discussed such as consequences of various forms of maximum principle, issues related to existence theory, and basic properties of singularities in the flow. A detailed exposition of Perelman's entropy functionals is combined with a description of Cheeger-Gromov-Hamilton compactness of manifolds and flows to show how a 'tangent' flow can be extracted from a singular Ricci flow. Finally, all these threads are pulled together to give a modern proof of Hamilton's theorem that a closed three-dimensional manifold whichcarries a metric of positive Ricci curvature is a spherical space form.
Table of Contents
- 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.
by "Nielsen BookData"