The Ricci flow : techniques and applications, Part I, geometric aspects / Bennett Chow, Sun-Chin Chu, David Glickenstein... [et al.]

Auteur principal : Chow, Bennett, 1962-, AuteurType de document : MonographieCollection : Mathematical surveys and monographs, 135Langue : anglais.Pays: Etats Unis.Éditeur : Providence : American Mathematical Society, 2007Description : 1 vol. (XXIII-536 p.) : glossaire ; 26 cmISBN: 9780821839461.ISSN: 0885-4653.Bibliographie : Bibliogr. p. 513-529. Notes bibliogr. Index.Sujet MSC : 53Exx, Differential geometry - Geometric evolution equations
35K55, PDEs - Parabolic equations and parabolic systems, Nonlinear parabolic equations
35K05, PDEs - Parabolic equations and parabolic systems, Heat equation
53C25, Global differential geometry, Special Riemannian manifolds (Einstein, Sasakian, etc.)
58J35, Global analysis, analysis on manifolds - PDEs on manifolds; differential operators, Heat and other parabolic equation methods
En-ligne : Zentralblatt | MathSciNet | AMS Item type: Monographie
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Bibliogr. p. 513-529. Notes bibliogr. Index

This book gives a presentation of topics in Hamilton's Ricci flow for graduate students and mathematicians interested in working in the subject. The authors have aimed at presenting technical material in a clear and detailed manner. In this volume, geometric aspects of the theory have been emphasized. The book presents the theory of Ricci solitons, Kähler-Ricci flow, compactness theorems, Perelman's entropy monotonicity and no local collapsing, Perelman's reduced distance function and applications to ancient solutions, and a primer of 3-manifold topology. Various technical aspects of Ricci flow have been explained in a clear and detailed manner. The authors have tried to make some advanced material accessible to graduate students and nonexperts. The book gives a rigorous introduction to Perelman's work and explains technical aspects of Ricci flow useful for singularity analysis. Throughout, there are appropriate references so that the reader may further pursue the statements and proofs of the various results. (source : AMS)

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