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The Ricci Flow: An Introduction
 
Bennett Chow University of California, San Diego, CA
Dan Knopf University of Texas, Austin, TX
Front Cover for The Ricci Flow: An Introduction
Available Formats:
Electronic ISBN: 978-1-4704-1337-8
Product Code: SURV/110.E
List Price: $97.00
MAA Member Price: $87.30
AMS Member Price: $77.60
Front Cover for The Ricci Flow: An Introduction
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  • Front Cover for The Ricci Flow: An Introduction
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The Ricci Flow: An Introduction
Bennett Chow University of California, San Diego, CA
Dan Knopf University of Texas, Austin, TX
Available Formats:
Electronic ISBN:  978-1-4704-1337-8
Product Code:  SURV/110.E
List Price: $97.00
MAA Member Price: $87.30
AMS Member Price: $77.60
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 1102004; 325 pp
    MSC: Primary 53; 58; 35; 57;

    The Ricci flow is a powerful technique that integrates geometry, topology, and analysis. Intuitively, the idea is to set up a PDE that evolves a metric according to its Ricci curvature. The resulting equation has much in common with the heat equation, which tends to “flow” a given function to ever nicer functions. By analogy, the Ricci flow evolves an initial metric into improved metrics.

    Richard Hamilton began the systematic use of the Ricci flow in the early 1980s and applied it in particular to study 3-manifolds. Grisha Perelman has made recent breakthroughs aimed at completing Hamilton's program.

    The Ricci flow method is now central to our understanding of the geometry and topology of manifolds. This book is an introduction to that program and to its connection to Thurston's geometrization conjecture.

    The authors also provide a “Guide for the hurried reader”, to help readers wishing to develop, as efficiently as possible, a nontechnical appreciation of the Ricci flow program for 3-manifolds, i.e., the so-called “fast track”.

    The book is suitable for geometers and others who are interested in the use of geometric analysis to study the structure of manifolds.

    The Ricci Flow was nominated for the 2005 Robert W. Hamilton Book Award, which is the highest honor of literary achievement given to published authors at the University of Texas at Austin.

    Readership

    Graduate students and research mathematicians interested in geometric analysis.

  • Table of Contents
     
     
    • Chapters
    • 1. The Ricci flow of special geometries
    • 2. Special and limit solutions
    • 3. Short time existence
    • 4. Maximum principles
    • 5. The Ricci flow on surfaces
    • 6. Three-manifolds of positive Ricci curvature
    • 7. Derivative estimates
    • 8. Singularities and the limits of their dilations
    • 9. Type I singularities
    • Appendix A. The Ricci calculus
    • Appendix B. Some results in comparison geometry
  • Additional Material
     
     
  • Reviews
     
     
    • Well written ... topics are well-motivated and presented with clarity and insight ... proofs are clear yet detailed so that the material is accessible to a wide audience as well as specialists. Gaps in arguments in the literature are filled in.

      Zentralblatt MATH
  • Request Review Copy
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Volume: 1102004; 325 pp
MSC: Primary 53; 58; 35; 57;

The Ricci flow is a powerful technique that integrates geometry, topology, and analysis. Intuitively, the idea is to set up a PDE that evolves a metric according to its Ricci curvature. The resulting equation has much in common with the heat equation, which tends to “flow” a given function to ever nicer functions. By analogy, the Ricci flow evolves an initial metric into improved metrics.

Richard Hamilton began the systematic use of the Ricci flow in the early 1980s and applied it in particular to study 3-manifolds. Grisha Perelman has made recent breakthroughs aimed at completing Hamilton's program.

The Ricci flow method is now central to our understanding of the geometry and topology of manifolds. This book is an introduction to that program and to its connection to Thurston's geometrization conjecture.

The authors also provide a “Guide for the hurried reader”, to help readers wishing to develop, as efficiently as possible, a nontechnical appreciation of the Ricci flow program for 3-manifolds, i.e., the so-called “fast track”.

The book is suitable for geometers and others who are interested in the use of geometric analysis to study the structure of manifolds.

The Ricci Flow was nominated for the 2005 Robert W. Hamilton Book Award, which is the highest honor of literary achievement given to published authors at the University of Texas at Austin.

Readership

Graduate students and research mathematicians interested in geometric analysis.

  • Chapters
  • 1. The Ricci flow of special geometries
  • 2. Special and limit solutions
  • 3. Short time existence
  • 4. Maximum principles
  • 5. The Ricci flow on surfaces
  • 6. Three-manifolds of positive Ricci curvature
  • 7. Derivative estimates
  • 8. Singularities and the limits of their dilations
  • 9. Type I singularities
  • Appendix A. The Ricci calculus
  • Appendix B. Some results in comparison geometry
  • Well written ... topics are well-motivated and presented with clarity and insight ... proofs are clear yet detailed so that the material is accessible to a wide audience as well as specialists. Gaps in arguments in the literature are filled in.

    Zentralblatt MATH
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