Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
Please make all selections above before adding to cart
Copy To Clipboard
Successfully Copied!
The Ricci Flow: Techniques and Applications: Part III: Geometric-Analytic Aspects

Bennett Chow University of California, San Diego, La Jolla, CA
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: 978-0-8218-4661-2
Product Code: SURV/163
List Price: $120.00 MAA Member Price:$108.00
AMS Member Price: $96.00 Electronic ISBN: 978-1-4704-1390-3 Product Code: SURV/163.E List Price:$113.00
MAA Member Price: $101.70 AMS Member Price:$90.40
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: $180.00 MAA Member Price:$162.00
AMS Member Price: $144.00 Click above image for expanded view The Ricci Flow: Techniques and Applications: Part III: Geometric-Analytic Aspects Bennett Chow University of California, San Diego, La Jolla, CA 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: 978-0-8218-4661-2 Product Code: SURV/163  List Price:$120.00 MAA Member Price: $108.00 AMS Member Price:$96.00
 Electronic ISBN: 978-1-4704-1390-3 Product Code: SURV/163.E
 List Price: $113.00 MAA Member Price:$101.70 AMS Member Price: $90.40 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:$180.00 MAA Member Price: $162.00 AMS Member Price:$144.00
• Book Details

Mathematical Surveys and Monographs
Volume: 1632010; 517 pp
MSC: Primary 53; 58; 35;

The Ricci flow uses methods from analysis to study the geometry and topology of manifolds. With the third part of their volume on techniques and applications of the theory, the authors give a presentation of Hamilton's Ricci flow for graduate students and mathematicians interested in working in the subject, with an emphasis on the geometric and analytic aspects.

The topics include Perelman's entropy functional, point picking methods, aspects of Perelman's theory of $\kappa$-solutions including the $\kappa$-gap theorem, compactness theorem and derivative estimates, Perelman's pseudolocality theorem, and aspects of the heat equation with respect to static and evolving metrics related to Ricci flow. In the appendices, we review metric and Riemannian geometry including the space of points at infinity and Sharafutdinov retraction for complete noncompact manifolds with nonnegative sectional curvature. As in the previous volumes, the authors have endeavored, as much as possible, to make the chapters independent of each other.

The book makes advanced material accessible to graduate students and nonexperts. It includes a rigorous introduction to some of Perelman's work and explains some technical aspects of Ricci flow useful for singularity analysis. The authors 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 geometric analysis, Ricci flow, Perelman's work on Poincaré.

• Chapters
• 1. Entropy, $\mu$-invariant, and finite time singularities
• 2. Geometric tools and point picking methods
• 3. Geometric properties of $\kappa$-solutions
• 4. Compactness of the space of $\kappa$-solutions
• 5. Perelman’s pseudolocality theorem
• 6. Tools used in proof of pseudolocality
• 7. Heat kernel for static metrics
• 8. Heat kernel for evolving metrics
• 9. Estimates of the heat equation for evolving metrics
• 10. Bounds for the heat kernel for evolving metrics
• 11. Elementary aspects of metric geometry
• 12. Convex functions on Riemannian manifolds
• 13. Asymptotic cones and Sharafutdinov retraction
• 14. Solutions to selected exercises

• 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: 1632010; 517 pp
MSC: Primary 53; 58; 35;

The Ricci flow uses methods from analysis to study the geometry and topology of manifolds. With the third part of their volume on techniques and applications of the theory, the authors give a presentation of Hamilton's Ricci flow for graduate students and mathematicians interested in working in the subject, with an emphasis on the geometric and analytic aspects.

The topics include Perelman's entropy functional, point picking methods, aspects of Perelman's theory of $\kappa$-solutions including the $\kappa$-gap theorem, compactness theorem and derivative estimates, Perelman's pseudolocality theorem, and aspects of the heat equation with respect to static and evolving metrics related to Ricci flow. In the appendices, we review metric and Riemannian geometry including the space of points at infinity and Sharafutdinov retraction for complete noncompact manifolds with nonnegative sectional curvature. As in the previous volumes, the authors have endeavored, as much as possible, to make the chapters independent of each other.

The book makes advanced material accessible to graduate students and nonexperts. It includes a rigorous introduction to some of Perelman's work and explains some technical aspects of Ricci flow useful for singularity analysis. The authors 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 geometric analysis, Ricci flow, Perelman's work on Poincaré.

• Chapters
• 1. Entropy, $\mu$-invariant, and finite time singularities
• 2. Geometric tools and point picking methods
• 3. Geometric properties of $\kappa$-solutions
• 4. Compactness of the space of $\kappa$-solutions
• 5. Perelman’s pseudolocality theorem
• 6. Tools used in proof of pseudolocality
• 7. Heat kernel for static metrics
• 8. Heat kernel for evolving metrics
• 9. Estimates of the heat equation for evolving metrics
• 10. Bounds for the heat kernel for evolving metrics
• 11. Elementary aspects of metric geometry
• 12. Convex functions on Riemannian manifolds
• 13. Asymptotic cones and Sharafutdinov retraction
• 14. Solutions to selected exercises
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
You may be interested in...
Please select which format for which you are requesting permissions.