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Lectures on the Ricci Flow by Peter Topping
Lectures on the Ricci Flow by Peter Topping
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Lectures on the Ricci Flow

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Description

Hamilton's Ricci flow has attracted considerable attention since its introduction in 1982, owing partly to its promise in addressing the Poincaré 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.

Author Biography:

Peter Topping is a Senior Lecturer in Mathematics at the University of Warwick.
Release date Australia
October 12th, 2006
Author
Audience
  • Professional & Vocational
Illustrations
22 Line drawings, unspecified
Pages
124
Dimensions
153x230x7
ISBN-13
9780521689472
Product ID
2012031

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