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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    View other formats and editions of Lectures on the Ricci Flow 325 London Mathematical Society Lecture Note Series Series Number 325 by Peter Topping

    Publisher: Cambridge University Press
    Publication Date: 10/12/2006 12:00:00 AM
    ISBN13: 9780521689472, 978-0521689472
    ISBN10: 0521689473
    Also in:
    Mathematics 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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