As on arXiv
Abstract
We estimate the number of ends of smooth and singular Ricci shrinkers focussing first on general ends and later on asymptotically conical ones. In particular, we obtain a variety of applications to sequences of Ricci shrinkers converging in a weak pointed sense to a possibly singular limit Ricci shrinker, for instance no new conical end can form in the limit.
Comments: V2: Final version with minor revisions. To appear in Selecta Math
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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Geometric Structure of Ends of Ricci Shrinkers
Topics Ricci solitons · Same authors Alessandro Bertellotti, Reto Buzano · Shared terms “Ricci shrinkers”, “sequence”
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Noncompact self-shrinkers for mean curvature flow with arbitrary genus
Topics Boundaries & non-compact · Same author Reto Buzano · Shared terms “conical ends”, “asymptotically conical”, “sequence”
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On the geometry of asymptotically conical Ricci shrinkers (I): weighted analysis
Topics Boundaries & non-compact, Ricci solitons · Shared terms “Ricci shrinkers”, “asymptotically conical”
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Closed mean curvature flows with asymptotically conical singularities
Topics Weak & singular flows, Boundaries & non-compact, Ricci solitons · Shared terms “asymptotically conical”
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Bubble-Tree Convergence and Local Diffeomorphism Finiteness for Gradient Ricci Shrinkers
Topics Ricci solitons · Same author Reto Buzano · Shared terms “Ricci shrinkers”, “sequence”
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Rigidity and ε-regularity theorems of Ricci shrinkers
Topics Boundaries & non-compact, Ricci solitons · Shared terms “Ricci shrinkers”
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On the geometry of asymptotically conical Ricci shrinkers (II): strong uniqueness
Topics Boundaries & non-compact, Ricci solitons · Shared terms “Ricci shrinkers”, “asymptotically conical”
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On the uniqueness of Ricci flows from certain Alexandrov spaces
Topics Weak & singular flows, Boundaries & non-compact · Shared terms “possibly singular”
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
- 12C.9After Perelman
Singular flows, the Smale conjecture, and Bamler’s theory.
- 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.