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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
Hamilton's Ricci Flow
Softcover ISBN:  978-1-4704-7369-3
Product Code:  GSM/77.S
List Price: $92.00
MAA Member Price: $82.80
AMS Member Price: $73.60
eBook ISBN:  978-1-4704-2111-3
Product Code:  GSM/77.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7369-3
eBook: ISBN:  978-1-4704-2111-3
Product Code:  GSM/77.S.B
List Price: $177.00 $134.50
MAA Member Price: $159.30 $121.05
AMS Member Price: $141.60 $107.60
Hamilton's Ricci Flow
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
Softcover ISBN:  978-1-4704-7369-3
Product Code:  GSM/77.S
List Price: $92.00
MAA Member Price: $82.80
AMS Member Price: $73.60
eBook ISBN:  978-1-4704-2111-3
Product Code:  GSM/77.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7369-3
eBook ISBN:  978-1-4704-2111-3
Product Code:  GSM/77.S.B
List Price: $177.00 $134.50
MAA Member Price: $159.30 $121.05
AMS Member Price: $141.60 $107.60
  • Book Details
     
     
    Graduate Studies in Mathematics
    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.

    This book is co-published with Science Press.

    Readership

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

  • Table of Contents
     
     
    • 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 publishers of book reviews
    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.

This book is co-published with Science Press.

Readership

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 publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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