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About this product
- DescriptionHamilton'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.
- Author BiographyPeter Topping is a Senior Lecturer in Mathematics at the University of Warwick.
- Author(s)Peter Topping
- PublisherCambridge University Press
- Date of Publication12/10/2006
- Series TitleLondon Mathematical Society Lecture Note Series
- Series Part/Volume Numberv. 325
- Place of PublicationCambridge
- Country of PublicationUnited Kingdom
- ImprintCambridge University Press
- Content Note22 b/w illus.
- Weight190 g
- Width152 mm
- Height228 mm
- Spine7 mm
- Series Edited byN. J. Hitchin
- Format DetailsTrade paperback (US)
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