Overview

In 1982, R. Hamilton introduced a nonlinear evolution equation for Riemannian metrics with the aim of finding canonical metrics on manifolds. This evolution equation is known as the Ricci flow, and it has since been used widely and with great success, most notably in Perelman's solution of the Poincare conjecture. Furthermore, various convergence theorems have been established. This book provides a concise introduction to the subject as well as a comprehensive account of the convergence theory for the Ricci flow. The proofs rely mostly on maximum principle arguments. Special emphasis is placed on preserved curvature conditions, such as positive isotropic curvature. One of the major consequences of this theory is the Differentiable Sphere Theorem: a compact Riemannian manifold whose sectional curvatures all lie in the interval (1,4] is diffeomorphic to a spherical space form. This question has a long history, dating back to a seminal paper by H. E. Rauch in 1951, and it was resolved in 2007 by the author and Richard Schoen. This text originated from graduate courses given at ETH Zurich and Stanford University, and is directed at graduate students and researchers. The reader is assumed to be familiar with basic Riemannian geometry, but no previous knowledge of Ricci flow is required.

Full Product Details

Author:   Simon Brendle
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Edition:   New ed.
Volume:   111
Weight:   0.480kg
ISBN:  

9780821849385

ISBN 10:   0821849387
Pages:   176
Publication Date:   28 February 2010
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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