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Book 11B

Solitons, Compactness and Singularities

Hamilton’s flow, part two

Ricci solitons, ancient solutions and the Harnack inequality, compactness of flows, the formation of singularities, and exactly what was missing in 2002.

  • Main companionThe Ricci Flow: An Introduction · Chow & Knopf
  • ReferenceHamilton’s Ricci Flow · Chow, Lu & Ni
In preparation

Contents

  1. 1
    Ricci Solitons

    Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.

    In preparation

  2. 2
    Ancient Solutions and the Harnack Inequality

    Comparing curvature across space and time.

    In preparation

  3. 3
    Compactness of Ricci Flows

    Hamilton’s compactness theorem and the missing injectivity radius bound.

    In preparation

  4. 4
    Singularities

    Blow-ups, neckpinches, degenerate neckpinches and the cigar problem.

    In preparation

  5. 5
    Hamilton’s Program in 2002

    What was proved, what was missing, and where Perelman came in.

    In preparation

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