
Preface  Preview Material  Table of Contents  Supplementary Material 
Graduate Studies in Mathematics 2006; 608 pp; hardcover Volume: 77 ISBN10: 0821842315 ISBN13: 9780821842317 List Price: US$86 Member Price: US$68.80 Order Code: GSM/77 See also: Ricci Flow and Geometrization of 3Manifolds  John W Morgan and Frederick TszHo Fong Low Dimensional Topology  Tomasz S Mrowka and Peter S Ozsvath LowDimensional 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 copublished with Science Press. Readership Graduate students and research mathematicians interested in geometric analysis, the Poincaré conjecture, Thurston's geometrization conjecture, and 3manifolds. Reviews "The style of the book is very pleasant, including lots of motivations and background material, course outlines and exercises (with solutions), the bibliography is rather comprehensive. This work is certain to become one of the main references in this field of great current interest."  M. Kunzinger "This book is a very well written introduction to and resource for study of the Ricci flow. It is quite selfcontained, 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 


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