
Preface  Preview Material  Table of Contents  Supplementary Material 
Mathematical Surveys and Monographs 2008; 458 pp; hardcover Volume: 144 ISBN10: 0821844296 ISBN13: 9780821844298 List Price: US$112 Member Price: US$89.60 Order Code: SURV/144 See also: The Ricci Flow: An Introduction  Bennett Chow and Dan Knopf The Ricci Flow: Techniques and Applications: Part I: Geometric Aspects  Bennett Chow, SunChin Chu, David Glickenstein, Christine Guenther, James Isenberg, Tom Ivey, Dan Knopf, Peng Lu, Feng Luo and Lei Ni The Ricci Flow: Techniques and Applications: Part III: GeometricAnalytic Aspects  Bennett Chow, SunChin Chu, David Glickenstein, Christine Guenther, James Isenberg, Tom Ivey, Dan Knopf, Peng Lu, Feng Luo and Lei Ni  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 heattype equations and systems on manifolds, the classification by Böhm and Wilking of closed manifolds with 2positive 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 LiYautype 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. See also:
Readership Graduate students and research mathematicians interested in geometic analysis; geometry and topology. Reviews "Just like in the first part this book is meant to be a text book as well as a reference book and it includes exercises as well as the solutions for some of them. The authors took a great care in making this a self contained book which compiles a great amount of data related to Ricci flow, organizing the information in a very clear way giving very often information on the content of each chapter and relating it to other parts of the book. An example is the sumary given in the preface, another more detailed sumary given in a special kind of chapter zero, also in the beginning of each chapter and sometimes introducing each section. Besides all this, each chapter includes a special section in the end with notes and commentaries. This approach gives the reader permanently a global view on the subject while the details are being explained. The book also includes a large number of exercises very often with suggestions for its resolutions."  Zentralblatt MATH "This book and this series is necessarily quite technical in parts, but it does reveal the full beauty and technical details of the Ricci flow. The authors should be congratulated on presenting such material in a very readable style, creating an excellent resource with thorough discussion of many aspects of Ricci flow for the benefit of mathematical researchers today and in the future."  Mathematical Reviews 


AMS Home 
Comments: webmaster@ams.org © Copyright 2014, American Mathematical Society Privacy Statement 