Paper · Feb 9, 2022
Preservation of product structures under the Ricci flow with instantaneous curvature bounds
As on arXiv
Abstract
In this note, we prove that there exists a constant , depending only on the dimension, such that if a complete solution to the Ricci flow splits as a product at time and has curvature bounded by , then the solution splits for all time.
- Submitted
- Feb 9, 2022
- Last revised
- Jan 31, 2025 (v2)
- Subjects
- math.DG
- Journal
- Commun. Anal. Geom., Vol. 32, Issue 10 (2024), pp. 2735-2755
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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.