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Zusatztext The approach here is somewhat different from that of Perelman. The author shows that the W-entropy and its monotonicity imply certain uniform Sobolev inequalities along Ricci flows. These are used in the proofs of the two steps mentioned above! bypassing the use of the reduced volume and reduced distance! which simplifies Perelman's proof considerably.-John Urbas! Mathematical Reviews! Issue 2011mThis is a very good book on Ricci flows. Anyone who is interested to know the most recent development in Ricci flows and the Poincaré conjecture should take a look at the book.-Zentralblatt MATH It is clear as vodka that! as Zhang advertises in the Preface! 'the first half of the book is aimed at graduate students and the second half is intended for researchers.' With some good timing! the same reader can start as one and continue as the other. ? a very important contribution to the genre.-MAA Reviews! September 2010 Informationen zum Autor Qi S. Zhang is a professor of mathematics at the University of California, Riverside. Klappentext This text introduces the field of analysis on Riemann manifolds and uses the tools of Sobolev imbedding and heat kernel estimates to study Ricci flows! especially with surgeries. Key ideas! difficult proofs! and important applications are explained in a succinct! accessible! and unified manner. Zusammenfassung Focusing on Sobolev inequalities and their applications to analysis on manifolds and Ricci flow, this title introduces the field of analysis on Riemann manifolds and uses the tools of Sobolev imbedding and heat kernel estimates to study Ricci flows, especially with surgeries. Inhaltsverzeichnis Introduction. Sobolev Inequalities in the Euclidean Space. Basics of Riemann Geometry. Sobolev Inequalities on Manifolds. Basics of Ricci Flow. Perelman’s Entropies and Sobolev Inequality. Ancient ? Solutions and Singularity Analysis. Sobolev Inequality with Surgeries. Applications to the Poincaré Conjecture. Bibliography. Index. ...
