ENGLISH

Hamilton's Ricci Flow

By Bennett Chow , Peng Lu , and Lei Ni

Book information

Publisher
American Mathematical Society
Year
2006
ISBN
9780821842317, 0821842315
Open Library ID
OL13637831M
Language
english
Format
DJVU
Filesize
6 MB (6078019 bytes)
Series
Graduate Studies in Mathematics
Pages
647\647
DPI
600
Scanned
no
Time added
2011-04-11 19:55:47

Description

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 Poincar???© conjecture and Thurston's geometrization conjecture.

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