The Ricci Flow : techniques and applications, Part II, analytic aspects / Bennett Chow, Sun-Chin Chu, David Glickenstein... [et al.]

Auteur principal : Chow, Bennett, 1962-, AuteurType de document : MonographieCollection : Mathematical surveys and monographs, 144Langue : anglais.Pays: Etats Unis.Éditeur : Providence : American Mathematical Society, 2008Description : 1 vol. (XXV-458 p.) ; 26 cmISBN: 9780821844298.ISSN: 0885-4653.Bibliographie : Bibliogr. p. 433-454. 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
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Bibliogr. p. 433-454. Index

Geometric analysis has become one of the most important tools in geometry and topology. In their books on the Ricci flow, the authors reveal the depth and breadth of this flow method for understanding the structure of manifolds. With the present book, the authors focus on the analytic aspects of Ricci flow.

Some highlights of the presentation are weak and strong maximum principles for scalar heat-type equations and systems on manifolds, the classification by Böhm and Wilking of closed manifolds with 2-positive curvature operator, Bando's result that solutions to the Ricci flow are real analytic in the space variables, Shi's local derivative of curvature estimates and some variants, and differential Harnack estimates of Li-Yau-type including Hamilton's matrix estimate for the Ricci flow and Perelman's estimate for fundamental solutions of the adjoint heat equation coupled to the Ricci flow.

The authors have tried to make some advanced material accessible to graduate students and nonexperts. The book gives a rigorous introduction to some of Perelman's work and explains some technical aspects of Ricci flow useful for singularity analysis. They have also attempted to give the appropriate references so that the reader may further pursue the statements and proofs of the various results. (source : AMS)

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