The Ricci Flow: Techniques and Applications - Part III: Geometric-Analytic Aspects (Hardcover)

The Ricci flow uses methods from analysis to study the geometry and topology of manifolds. With the third part of their volume on techniques and applications of the theory, the authors give a presentation of Hamilton's Ricci flow for graduate students and mathematicians interested in working in the subject, with an emphasis on the geometric and analytic aspects. The topics include Perelman's entropy functional, point picking methods, aspects of Perelman's theory of κ -solutions including the κ -gap theorem, compactness theorem and derivative estimates, Perelman's pseudolocality theorem, and aspects of the heat equation with respect to static and evolving metrics related to Ricci flow. In the appendices, we review metric and Riemannian geometry including the space of points at infinity and Sharafutdinov retraction for complete noncompact manifolds with nonnegative sectional curvature. As in the previous volumes, the authors have endeavored, as much as possible, to make the chapters independent of each other. The book makes advanced material accessible to graduate students and nonexperts. It includes a rigorous introduction to some of Perelman's work and explains some technical aspects of Ricci flow useful for singularity analysis. The authors give the appropriate references so that the reader may further pursue the statements and proofs of the various results.

General

Imprint:	American Mathematical Society
Country of origin:	United States
Series:	Mathematical Surveys and Monographs
Release date:	May 2010
First published:	2010
Authors:	Bennett Chow
Dimensions:	189 x 319 x 32mm (L x W x T)
Format:	Hardcover
Pages:	517
ISBN-13:	978-0-8218-4661-2
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > General Promotions
LSN:	0-8218-4661-2
Barcode:	9780821846612

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