The Ricci flow : an introduction / Bennett Chow, Dan Knopf

Auteur principal : Chow, Bennett, 1962-, AuteurCo-auteur : Knopf, Dan, 1959-, AuteurType de document : MonographieCollection : Mathematical surveys and monographs, 110Langue : anglais.Pays: Etats Unis.Éditeur : Providence : American Mathematical Society, 2004Description : 1 vol. (XII-325 p.) : fig. ; 26 cmISBN: 0821835157.ISSN: 0885-4653.Bibliographie : Bibliogr. p. 317-322. Index.Sujet MSC : 53Exx, Differential geometry - Geometric evolution equations
35K55, PDEs - Parabolic equations and parabolic systems, Nonlinear parabolic equations
53-02, Research exposition (monographs, survey articles) pertaining to differential geometry
58J35, Global analysis, analysis on manifolds - PDEs on manifolds; differential operators, Heat and other parabolic equation methods
57M50, Manifolds and cell complexes - General low-dimensional topology, General geometric structures on low-dimensional manifolds
En-ligne : Zentralblatt | MathSciNet | AMS
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Bibliogr. p. 317-322. Index

The Ricci flow is a powerful technique that integrates geometry, topology, and analysis. Intuitively, the idea is to set up a PDE that evolves a metric according to its Ricci curvature. The resulting equation has much in common with the heat equation, which tends to "flow" a given function to ever nicer functions. By analogy, the Ricci flow evolves an initial metric into improved metrics.

Richard Hamilton began the systematic use of the Ricci flow in the early 1980s and applied it in particular to study 3-manifolds. Grisha Perelman has made recent breakthroughs aimed at completing Hamilton's program.

The Ricci flow method is now central to our understanding of the geometry and topology of manifolds. This book is an introduction to that program and to its connection to Thurston's geometrization conjecture.

The authors also provide a "Guide for the hurried reader", to help readers wishing to develop, as efficiently as possible, a nontechnical appreciation of the Ricci flow program for 3-manifolds, i.e., the so-called "fast track".

The book is suitable for geometers and others who are interested in the use of geometric analysis to study the structure of manifolds. (source : AMS)

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