Paper · Oct 19, 2020

Hamilton type entropy formula along the Ricci flow on surfaces with boundary

Keita Kunikawa, Yohei Sakurai

math.DGarXiv:2010.09179v2
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Abstract

In this article, we establish a monotonicity formula of Hamilton type entropy along Ricci flow on compact surfaces with boundary. We also study the relation between our entropy functional and the -functional of Perelman type.

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Submitted
Oct 19, 2020
Last revised
Jul 7, 2021 (v2)
Subjects
math.DG

Comments: 9 pages

Ricci flowSurfaces

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  1. Gaussian heat kernel estimates of Bamler-Zhang type along super Ricci flow

    Keita Kunikawa and Yohei Sakurai

    Topics Ricci flow · Same authors Keita Kunikawa, Yohei Sakurai

  2. Liouville theorem for heat equation along ancient super Ricci flow via reduced geometry

    Keita Kunikawa and Yohei Sakurai

    Topics Ricci flow · Same authors Keita Kunikawa, Yohei Sakurai · Shared terms “Perelman”

  3. Liouville theorems for harmonic map heat flow along ancient super Ricci flow via reduced geometry

    Keita Kunikawa and Yohei Sakurai

    Topics Ricci flow · Same authors Keita Kunikawa, Yohei Sakurai · Shared terms “Perelman”

  4. Almost splitting and quantitative stratification for super Ricci flow

    Keita Kunikawa and Yohei Sakurai

    Topics Ricci flow · Same authors Keita Kunikawa, Yohei Sakurai

  5. Monotonicity of the Liouville entropy along the Ricci flow on surfaces

    Karen Butt, Alena Erchenko, Tristan Humbert et al.

    Topics Surfaces · Shared terms “entropy along”

  6. Notes on harmonic-Ricci flow on surface

    Xiang-Zhi Cao

    Topics Surfaces

  7. Variations of the harmonic entropy and linear drift on negatively curved surfaces

    Karen Butt, Alena Erchenko and Tristan Humbert

    Topics Surfaces

  8. A normalized Ricci flow on surfaces with boundary towards the complete hyperbolic metric

    Gang Li

    Topics Surfaces · Shared terms “compact surfaces”

Read around it

Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

Ricci flow Hamilton's Ricci flow evolves a Riemannian metric by minus twice its Ricci curvature. It is a nonlinear heat equation for geometry: it spreads… Start with: Three-manifolds with positive Ricci curvature (Hamilton, 1982) Surfaces On surfaces Ricci flow is conformal and scalar. It gives a heat-flow proof of the uniformization theorem: every closed surface converges to constant… Start with: The Ricci flow on surfaces (Hamilton, 1988)

In the guidebook

  1. 5A.5
    Uniformization and the Two-Dimensional Ricci FlowBook 5A · Complex Analysis and Conformal Geometry

    Constant-curvature metrics on surfaces, and Ricci flow as a heat equation for the conformal factor.

  2. 11A.12
    Ricci Flow on SurfacesBook 11A · The Ricci Flow: Existence and Maximum Principles

    Uniformization by Ricci flow, and Hamilton’s entropy.

  3. 10A.12
    Curve Shortening and Minimal DiscsBook 10A · Three-Manifolds and Geometrization

    How loops shrink under curvature, how the discs they bound lose area, and Perelman's extinction estimate.