Lectures on the Ricci Flow

Hamilton's Ricci flow has attracted considerable attention since its introduction in 1982, owing partly to its promise in addressing the Poincar 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 which carries a metric of positive Ricci curvature is a spherical space form.

Author: Peter Topping
Publisher: Cambridge University Press
Published: 11/06/2006
Pages: 124
Binding Type: Paperback
Weight: 0.43lbs
Size: 9.06h x 6.02w x 0.28d
ISBN: 9780521689472

About the Author
Topping, Peter: - Peter Topping is a Senior Lecturer in Mathematics at the University of Warwick.

This title is not returnable