Paper · Sep 12, 2018
On the regular-convexity of Ricci shrinker limit spaces
As on arXiv
Abstract
In this paper, we study the structure of the pointed-Gromov-Hausdorff limits of sequences of Ricci shrinkers. We define a regular-singular decomposition following the work of Cheeger-Colding for manifolds with a uniform Ricci curvature lower bound, and prove that the regular part of any Ricci shrinker limit space is convex, inspired by Colding-Naber's original idea of parabolic smoothing of the distance functions.
- Submitted
- Sep 12, 2018
- Last revised
- May 27, 2020 (v2)
- Subjects
- math.DG
Comments: revised version, to appear in J. Reine Angew. Math
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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.
In the guidebook
- 6C.11Optimal Transport and Ricci Curvature
Kantorovich duality, Wasserstein geometry, the heat equation as a gradient flow of entropy, displacement convexity, and Ricci curvature as convexity, from Lott–Sturm–Villani to McCann–Topping and the reduced volume.
- 9B.4Convergence of Manifolds
Gromov–Hausdorff and Cheeger–Gromov convergence, and the compactness theorem.
- 11B.3Compactness of Ricci Flows
Hamilton’s compactness theorem and the missing injectivity radius bound.