The Ricci Flow: Techniques and Applications

Bennett Chow

ISBN 10: 0821846612 / ISBN 13: 9780821846612

Editore: American Mathematical Society, US, 2010

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The Ricci flow uses methods from analysis to study the geometry and topology of manifolds. With the third part of their volume on techniques and applications of the theory, the authors give a presentation of Hamilton's Ricci flow for graduate students and mathematicians interested in working in the subject, with an emphasis on the geometric and analytic aspects.The topics include Perelman's entropy functional, point picking methods, aspects of Perelman's theory of ? -solutions including the ? -gap theorem, compactness theorem and derivative estimates, Perelman's pseudolocality theorem, and aspects of the heat equation with respect to static and evolving metrics related to Ricci flow. In the appendices, we review metric and Riemannian geometry including the space of points at infinity and Sharafutdinov retraction for complete noncompact manifolds with nonnegative sectional curvature. As in the previous volumes, the authors have endeavored, as much as possible, to make the chapters independent of each other.The book makes advanced material accessible to graduate students and nonexperts. It includes a rigorous introduction to some of Perelman's work and explains some technical aspects of Ricci flow useful for singularity analysis. The authors give the appropriate references so that the reader may further pursue the statements and proofs of the various results.

Codice articolo LU-9780821846612

Dati bibliografici

• Titolo: The Ricci Flow: Techniques and Applications
• Editore: American Mathematical Society, US
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 0821846612
• ISBN 13: 9780821846612
• Rilegatura: Hardback
• Condizione: New
• Dimensioni: 18,42 L x 3,18 A x 26,04 P centimetri 18,42 centimetri di larghezza per 3,18 centimetri di altezza per 26,04 centimetri di profondità
• Peso: 1118 grammi

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Riassunto

When we last saw our friends, geometric topics ware in one volume and analytic topics in the next, and it was not clear that they would ever ever find each other. Well, here they are, safe and sound, together at last, and already as far chapter 17. The topics include entropy, u-invariant, and finite time singularities; geometric tools and point picking methods; geometric properties of k-solutions; the compactness of the space of k-solutions; Perelman's pseudo-locality theorem; tools used in the proof of pseudo-locality; heat kernel for static metrics and for evolving metrics; estimates of the heat equation for evolving metrics; and bounds for the heat kernel for evolving metrics. Solutions are provided for selected exercises. The three parts are paged and indexed separately. Annotation ©2010 Book News, Inc., Portland, OR (booknews.com)