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The Ricci Flow: Techniques and Applications: Part II: Analytic Aspects

Bennett Chow University of California, San Diego, La Jolla, CA and East China Normal University, Shanghai, People’s Republic of China
Sun-Chin Chu National Chung Cheng University, Chia-Yi, Taiwan
David Glickenstein University of Arizona, Tucson, AZ
Christine Guenther Pacific University, Forest Grove, OR
James Isenberg University of Oregon, Eugene, OR
Tom Ivey College of Charleston, Charleston, SC
Dan Knopf University of Texas, Austin, Austin, TX
Peng Lu University of Oregon, Eugene, OR
Feng Luo Rutgers University, Piscataway, NJ
Lei Ni University of California, San Diego, La Jolla, CA
Available Formats:
Hardcover ISBN: 978-0-8218-4429-8
Product Code: SURV/144
List Price: $119.00 MAA Member Price:$107.10
AMS Member Price: $95.20 Electronic ISBN: 978-1-4704-1371-2 Product Code: SURV/144.E List Price:$112.00
MAA Member Price: $100.80 AMS Member Price:$89.60
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List Price: $178.50 MAA Member Price:$160.65
AMS Member Price: $142.80 Click above image for expanded view The Ricci Flow: Techniques and Applications: Part II: Analytic Aspects Bennett Chow University of California, San Diego, La Jolla, CA and East China Normal University, Shanghai, People’s Republic of China Sun-Chin Chu National Chung Cheng University, Chia-Yi, Taiwan David Glickenstein University of Arizona, Tucson, AZ Christine Guenther Pacific University, Forest Grove, OR James Isenberg University of Oregon, Eugene, OR Tom Ivey College of Charleston, Charleston, SC Dan Knopf University of Texas, Austin, Austin, TX Peng Lu University of Oregon, Eugene, OR Feng Luo Rutgers University, Piscataway, NJ Lei Ni University of California, San Diego, La Jolla, CA Available Formats:  Hardcover ISBN: 978-0-8218-4429-8 Product Code: SURV/144  List Price:$119.00 MAA Member Price: $107.10 AMS Member Price:$95.20
 Electronic ISBN: 978-1-4704-1371-2 Product Code: SURV/144.E
 List Price: $112.00 MAA Member Price:$100.80 AMS Member Price: $89.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$178.50 MAA Member Price: $160.65 AMS Member Price:$142.80
• Book Details

Mathematical Surveys and Monographs
Volume: 1442008; 458 pp
MSC: Primary 53; 58; 35;

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.

Graduate students and research mathematicians interested in geometic analysis; geometry and topology.

• Chapters
• 10. Weak maximum principles for scalars, tensors, and systems
• 11. Closed manifolds with positive curvature
• 12. Weak and strong maximum principles on noncompact manifolds
• 13. Qualitative behavior of classes of solutions
• 14. Local derivative of curvature estimates
• 15. Differential Harnack estimates of LYH-type
• 16. Perelman’s differential Harnack estimate

• 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1442008; 458 pp
MSC: Primary 53; 58; 35;

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.

Graduate students and research mathematicians interested in geometic analysis; geometry and topology.

• Chapters
• 10. Weak maximum principles for scalars, tensors, and systems
• 11. Closed manifolds with positive curvature
• 12. Weak and strong maximum principles on noncompact manifolds
• 13. Qualitative behavior of classes of solutions
• 14. Local derivative of curvature estimates
• 15. Differential Harnack estimates of LYH-type
• 16. Perelman’s differential Harnack estimate
• 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
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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