Description

Book Synopsis
Hamilton's Ricci flow has attracted considerable attention since its introduction in 1982, owing partly to its promise in addressing the Poincaré conjecture and Thurston's geometrization conjecture. This book gives a concise introduction to the subject with the hindsight of Perelman's breakthroughs from 2002/2003.

Trade Review
"... The freedom to skip some of the proofs, and the lucid presentation, this small book is pleasant to read." Peng Lu, Mathematical Reviews

Table of Contents
1. Introduction; 2. Riemannian geometry background; 3. The maximum principle; 4. Comments on existence theory for parabolic PDE; 5. Existence theory for the Ricci flow; 6. Ricci flow as a gradient flow; 7. Compactness of Riemannian manifolds and flows; 8. Perelman's W entropy functional; 9. Curvature pinching and preserved curvature properties under Ricci flow; 10. Three-manifolds with positive Ricci curvature and beyond.

Lectures on the Ricci Flow 325 London Mathematical Society Lecture Note Series Series Number 325

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    A Paperback by Peter Topping

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      Book details

      Publisher Cambridge University Press
      Published 10 December 2006
      ISBN-13 9780521689472
      978-0521689472
      ISBN-10 0521689473
      Also in:
      Topology

      Description

      Book Synopsis
      Hamilton's Ricci flow has attracted considerable attention since its introduction in 1982, owing partly to its promise in addressing the Poincaré conjecture and Thurston's geometrization conjecture. This book gives a concise introduction to the subject with the hindsight of Perelman's breakthroughs from 2002/2003.

      Trade Review
      "... The freedom to skip some of the proofs, and the lucid presentation, this small book is pleasant to read." Peng Lu, Mathematical Reviews

      Table of Contents
      1. Introduction; 2. Riemannian geometry background; 3. The maximum principle; 4. Comments on existence theory for parabolic PDE; 5. Existence theory for the Ricci flow; 6. Ricci flow as a gradient flow; 7. Compactness of Riemannian manifolds and flows; 8. Perelman's W entropy functional; 9. Curvature pinching and preserved curvature properties under Ricci flow; 10. Three-manifolds with positive Ricci curvature and beyond.

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