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Hamilton’s Ricci Flow

Bennett Chow University of California, San Diego, La Jolla, CA
Peng Lu University of Oregon, Eugene, OR
Lei Ni University of California, San Diego, La Jolla, CA
A co-publication of the AMS and Science Press
Available Formats:
Hardcover ISBN: 978-0-8218-4231-7
Product Code: GSM/77
List Price: $92.00 MAA Member Price:$82.80
AMS Member Price: $73.60 Electronic ISBN: 978-1-4704-2111-3 Product Code: GSM/77.E List Price:$86.00
MAA Member Price: $77.40 AMS Member Price:$68.80
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: $138.00 MAA Member Price:$124.20
AMS Member Price: $110.40 Click above image for expanded view Hamilton’s Ricci Flow Bennett Chow University of California, San Diego, La Jolla, CA Peng Lu University of Oregon, Eugene, OR Lei Ni University of California, San Diego, La Jolla, CA A co-publication of the AMS and Science Press Available Formats:  Hardcover ISBN: 978-0-8218-4231-7 Product Code: GSM/77  List Price:$92.00 MAA Member Price: $82.80 AMS Member Price:$73.60
 Electronic ISBN: 978-1-4704-2111-3 Product Code: GSM/77.E
 List Price: $86.00 MAA Member Price:$77.40 AMS Member Price: $68.80 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:$138.00 MAA Member Price: $124.20 AMS Member Price:$110.40
• Book Details

Volume: 772006; 608 pp
MSC: Primary 53; 58; 35;

Ricci flow is a powerful analytic method for studying the geometry and topology of manifolds. This book is an introduction to Ricci flow for graduate students and mathematicians interested in working in the subject. To this end, the first chapter is a review of the relevant basics of Riemannian geometry. For the benefit of the student, the text includes a number of exercises of varying difficulty.

The book also provides brief introductions to some general methods of geometric analysis and other geometric flows. Comparisons are made between the Ricci flow and the linear heat equation, mean curvature flow, and other geometric evolution equations whenever possible.

Several topics of Hamilton's program are covered, such as short time existence, Harnack inequalities, Ricci solitons, Perelman's no local collapsing theorem, singularity analysis, and ancient solutions.

A major direction in Ricci flow, via Hamilton's and Perelman's works, is the use of Ricci flow as an approach to solving the Poincaré conjecture and Thurston's geometrization conjecture.

Graduate students and research mathematicians interested in geometric analysis, the Poincaré conjecture, Thurston's geometrization conjecture, and 3-manifolds.

• Chapters
• Chapter 1. Riemannian geometry
• Chapter 2. Fundamentals of the Ricci flow equation
• Chapter 3. Closed 3-manifolds with positive Ricci curvature
• Chapter 4. Ricci solitons and special solutions
• Chapter 5. Isoperimetric estimates and no local collapsing
• Chapter 6. Preparation for singularity analysis
• Chapter 7. High-dimensional and noncompact Ricci flow
• Chapter 8. Singularity analysis
• Chapter 9. Ancient solutions
• Chapter 10. Differential Harnack estimates
• Chapter 11. Space-time geometry
• Appendix A. Geometric analysis related to Ricci flow
• Appendix B. Analytic techniques for geometric flows
• Appendix S. Solutions to selected exercises

• Reviews

• The style of the book is very pleasant, including lots of motivations and background material, course outlines and exercises (with solutions), the bibliography is rather comprehensive. This work is certain to become one of the main references in this field of great current interest.

M. Kunzinger
• This book is a very well written introduction to and resource for study of the Ricci flow. It is quite self-contained, but relevant references are provided at appropriate points. The style of the book renders it accessible to graduate students (suggested course outlines and many relevant further references are provided), while its substance provides an essential resource for background, key concepts and fundamental ideas for further study in the area.

James McCoy, Mathematical Reviews
• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 772006; 608 pp
MSC: Primary 53; 58; 35;

Ricci flow is a powerful analytic method for studying the geometry and topology of manifolds. This book is an introduction to Ricci flow for graduate students and mathematicians interested in working in the subject. To this end, the first chapter is a review of the relevant basics of Riemannian geometry. For the benefit of the student, the text includes a number of exercises of varying difficulty.

The book also provides brief introductions to some general methods of geometric analysis and other geometric flows. Comparisons are made between the Ricci flow and the linear heat equation, mean curvature flow, and other geometric evolution equations whenever possible.

Several topics of Hamilton's program are covered, such as short time existence, Harnack inequalities, Ricci solitons, Perelman's no local collapsing theorem, singularity analysis, and ancient solutions.

A major direction in Ricci flow, via Hamilton's and Perelman's works, is the use of Ricci flow as an approach to solving the Poincaré conjecture and Thurston's geometrization conjecture.

Graduate students and research mathematicians interested in geometric analysis, the Poincaré conjecture, Thurston's geometrization conjecture, and 3-manifolds.

• Chapters
• Chapter 1. Riemannian geometry
• Chapter 2. Fundamentals of the Ricci flow equation
• Chapter 3. Closed 3-manifolds with positive Ricci curvature
• Chapter 4. Ricci solitons and special solutions
• Chapter 5. Isoperimetric estimates and no local collapsing
• Chapter 6. Preparation for singularity analysis
• Chapter 7. High-dimensional and noncompact Ricci flow
• Chapter 8. Singularity analysis
• Chapter 9. Ancient solutions
• Chapter 10. Differential Harnack estimates
• Chapter 11. Space-time geometry
• Appendix A. Geometric analysis related to Ricci flow
• Appendix B. Analytic techniques for geometric flows
• Appendix S. Solutions to selected exercises
• The style of the book is very pleasant, including lots of motivations and background material, course outlines and exercises (with solutions), the bibliography is rather comprehensive. This work is certain to become one of the main references in this field of great current interest.

M. Kunzinger
• This book is a very well written introduction to and resource for study of the Ricci flow. It is quite self-contained, but relevant references are provided at appropriate points. The style of the book renders it accessible to graduate students (suggested course outlines and many relevant further references are provided), while its substance provides an essential resource for background, key concepts and fundamental ideas for further study in the area.

James McCoy, Mathematical Reviews
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
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