AMS Bookstore LOGO amslogo
Return to List

AMS TextbooksAMS Applications-related Books

Hamilton's Ricci Flow
Bennett Chow, University of California, San Diego, La Jolla, CA, Peng Lu, University of Oregon, Eugene, OR, and Lei Ni, University of California, San Diego, La Jolla, CA
A co-publication of the AMS and Science Press.
cover
SEARCH THIS BOOK:

Graduate Studies in Mathematics
2006; 608 pp; hardcover
Volume: 77
ISBN-10: 0-8218-4231-5
ISBN-13: 978-0-8218-4231-7
List Price: US$81
Member Price: US$64.80
Order Code: GSM/77
[Add Item]
See also:

Ricci Flow and Geometrization of 3-Manifolds - John W Morgan and Frederick Tsz-Ho Fong

Low Dimensional Topology - Tomasz S Mrowka and Peter S Ozsvath

Low-Dimensional Geometry: From Euclidean Surfaces to Hyperbolic Knots - Francis Bonahon

Ricci flow is a powerful analytic method for studying the geometry and topology of manifolds. This book is an introduction to Ricci flow for graduate students and mathematicians interested in working in the subject. To this end, the first chapter is a review of the relevant basics of Riemannian geometry. For the benefit of the student, the text includes a number of exercises of varying difficulty.

The book also provides brief introductions to some general methods of geometric analysis and other geometric flows. Comparisons are made between the Ricci flow and the linear heat equation, mean curvature flow, and other geometric evolution equations whenever possible.

Several topics of Hamilton's program are covered, such as short time existence, Harnack inequalities, Ricci solitons, Perelman's no local collapsing theorem, singularity analysis, and ancient solutions.

A major direction in Ricci flow, via Hamilton's and Perelman's works, is the use of Ricci flow as an approach to solving the Poincaré conjecture and Thurston's geometrization conjecture.

This book is co-published with Science Press.

Readership

Graduate students and research mathematicians interested in geometric analysis, the Poincaré conjecture, Thurston's geometrization conjecture, and 3-manifolds.

Reviews

"This book is a very well written introduction to and resource for study of the Ricci flow. It is quite self-contained, but relevant references are provided at appropriate points. The style of the book renders it accessible to graduate students (suggested course outlines and many relevant further references are provided), while its substance provides an essential resource for background, key concepts and fundamental ideas for further study in the area."

-- James McCoy, Mathematical Reviews

Powered by MathJax

  AMS Home | Comments: webmaster@ams.org
© Copyright 2014, American Mathematical Society
Privacy Statement

AMS Social

AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia