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Book 12A

Entropy and Noncollapsing

Perelman, part one

Ricci flow as a gradient flow, the 𝓦-entropy, κ-noncollapsing, reduced distance and reduced volume, and pseudolocality.

  • Primary sourceThe entropy formula for the Ricci flow · Grisha Perelman
  • Main companionNotes on Perelman’s Papers · Kleiner & Lott
In preparation

Contents

  1. 1
    How to Read Perelman

    The preprints, the expositions, and a method for reading them side by side.

    In preparation

  2. 2
    Ricci Flow as a Gradient Flow

    The 𝓕 functional, its monotonicity, and no steady breathers.

    In preparation

  3. 3
    The 𝓦-Entropy

    A scale-invariant entropy, log-Sobolev, and no shrinking breathers.

    In preparation

  4. 4
    κ-Noncollapsing

    The theorem that excludes the cigar.

    In preparation

  5. 5
    Reduced Distance and Reduced Volume

    A space-time Bishop–Gromov theorem.

    In preparation

  6. 6
    Pseudolocality

    Almost-Euclidean regions stay controlled, and the Harnack inequality behind it.

    In preparation

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