As on arXiv
Abstract
In this paper, we prove that the round cylinders are rigid in the space of Ricci shrinkers. Namely, any Ricci shrinker that is sufficiently close to in the pointed-Gromov-Hausdorff topology must itself be isometric to .
Comments: Revised version, accepted by Journal of Differential Geometry
Its neighbourhood
Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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Rigidity of complex projective spaces in Ricci shrinkers
Topics Limit spaces & RCD, Stability & uniqueness, Ricci solitons · Same author Yu Li · Shared terms “Ricci shrinkers”, “sufficiently close”, “Gromov Hausdorff”
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On the rigidity of Ricci shrinkers
Topics Limit spaces & RCD, Stability & uniqueness, Ricci solitons · Same author Yu Li · Shared terms “Ricci shrinkers”, “Hausdorff topology”, “pointed Gromov”
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Heat kernel on Ricci shrinkers (II)
Topics Limit spaces & RCD, Ricci solitons · Same authors Yu Li, Bing Wang · Shared terms “Ricci shrinkers”
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On the geometry of asymptotically conical Ricci shrinkers (I): weighted analysis
Topics Limit spaces & RCD, Stability & uniqueness, Ricci solitons · Same author Yu Li · Shared terms “Ricci shrinkers”, “pointed Gromov”, “Gromov Hausdorff”
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On Kähler Ricci shrinker surfaces
Topics Ricci solitons · Same authors Yu Li, Bing Wang · Shared terms “Ricci shrinkers”
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Non-collapsing of Ricci shrinkers with bounded curvature
Topics Limit spaces & RCD, Ricci solitons · Same author Yu Li · Shared terms “Ricci shrinkers”
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Gromov-Hausdorff Limits of Noncollapsed Kähler-Ricci Flows and the Geometry of Ricci Shrinkers
Topics Limit spaces & RCD, Stability & uniqueness, Ricci solitons · Same author Yu Li · Shared terms “Ricci shrinkers”, “Gromov Hausdorff”, “pointed Gromov”
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Uniqueness of Kähler Ricci shrinkers on toric orbifolds
Topics Stability & uniqueness, Ricci solitons · Same author Yu Li · Shared terms “Ricci shrinkers”
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.