ISBN-10:
0821844296
ISBN-13:
9780821844298
Pub. Date:
01/20/2008
Publisher:
American Mathematical Society
The Ricci Flow: Techniques and Applications

The Ricci Flow: Techniques and Applications

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Overview

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 Bohm 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. Also in the Mathematical Surveys and Monographs series: The Ricci Flow: An Introduction, Bennett Chow and Dan Knopf, Vol. 110, 2004. The Ricci Flow: Techniques and Applications. Part I: Geometric Aspects, Bennett Chow, Sun-Chin Chu, David Glickenstein, Christine Guenther, James Isenberg, Tom Ivey, Dan Knopf, Peng Lu, Feng Luo, and Lei Ni, Vol. 135, 2007. The Ricci Flow: Techniques and Applications. Part III: Geometric-Analytic Aspects, Bennett Chow, Sun-Chin Chu, David Glickenstein, Christine Guenther, James Isenberg, Tom Ivey, Dan Knopf, Peng Lu, Feng Luo, and Lei Ni (forthcoming).

Product Details

ISBN-13: 9780821844298
Publisher: American Mathematical Society
Publication date: 01/20/2008
Series: Mathematical Surveys and Monographs , #144
Edition description: New Edition
Pages: 458
Product dimensions: 7.00(w) x 10.30(h) x 1.10(d)

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