Paper · Jan 2, 2020
Uniform Lipschitz continuity of the isoperimetric profile of compact surfaces under normalized Ricci flow
As on arXiv
Abstract
We show that the isoperimetric profile of a compact Riemannian manifold is jointly continuous when metrics vary continuously. We also show that, when is a compact surface and evolves under normalized Ricci flow, is uniform Lipschitz continuous and hence is uniform locally Lipschitz continuous.
- Submitted
- Jan 2, 2020
- Last revised
- Oct 12, 2020 (v2)
- Subjects
- math.DG
Comments: 17 pages; Made minor corrections to Theorem 1.2 and Corollary 1.3
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Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 5A.5Uniformization and the Two-Dimensional Ricci Flow
Constant-curvature metrics on surfaces, and Ricci flow as a heat equation for the conformal factor.
- 10A.12Curve Shortening and Minimal Discs
How loops shrink under curvature, how the discs they bound lose area, and Perelman's extinction estimate.
- 11A.1The Equation and Its First Solutions
A heat equation for the metric: spheres, cylinders and scaling.