As on arXiv
Abstract
In this paper, we study the rigidity and ε-regularity theorems of Ricci shrinkers. First we prove the rigidity of the asymptotic volume ratio and local volume around a base point of a non-compact Ricci shrinker. Next we obtain some ε-regularity theorems of local entropy and curvature, which improve the previous corresponding results essentially and use them to study the structure of Ricci shrinkers at infinity. Especially, if the curvature of a non-compact Ricci shrinker satisfies some natural integral conditions, then it is asymptotic to a cone.
Comments: 31 papers
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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 and gap theorems for Ricci shrinkers
Topics Stability & uniqueness, Ricci solitons · Shared terms “Ricci shrinkers”
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On the geometry of asymptotically conical Ricci shrinkers (I): weighted analysis
Topics Boundaries & non-compact, Stability & uniqueness, Ricci solitons · Shared terms “Ricci shrinkers”
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On the rigidity of Ricci shrinkers
Topics Stability & uniqueness, Ricci solitons · Shared terms “Ricci shrinkers”, “compact Ricci”
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Ends of (singular) Ricci shrinkers
Topics Boundaries & non-compact, Ricci solitons · Shared terms “Ricci shrinkers”
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Rigidity of the round cylinders in Ricci shrinkers
Topics Stability & uniqueness, Ricci solitons · Shared terms “Ricci shrinkers”
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Heat kernel on Ricci shrinker metric measure spaces
Topics Ricci solitons · Same author Jie Wang · Shared terms “Ricci shrinkers”
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Rigidity of complex projective spaces in Ricci shrinkers
Topics Stability & uniqueness, Ricci solitons · Shared terms “Ricci shrinkers”
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Rigidity results for shrinking and expanding Ricci solitons
Topics Boundaries & non-compact, Stability & uniqueness, Ricci solitons
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
- 11B.1Ricci Solitons
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.
- 12B.2The Asymptotic Soliton and Three-Dimensional Shrinkers
Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.