As on arXiv
Abstract
We establish a uniform entropy bound for simply connected Ricci shrinkers with a finite second homotopy group and a uniform curvature bound. Additionally, we extend the non-collapsing result to a broader class of smooth metric measure spaces satisfying Bakry-Émery conditions.
Comments: 35 pages
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 the round cylinders in Ricci shrinkers
Topics Limit spaces & RCD, Ricci solitons · Same author Yu Li · Shared terms “Ricci shrinkers”
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Rigidity of complex projective spaces in Ricci shrinkers
Topics Limit spaces & RCD, Ricci solitons · Same author Yu Li · Shared terms “Ricci shrinkers”
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On the structure of noncollapsed Ricci flow limit spaces
Topics (Non)collapsing, Limit spaces & RCD · Same author Yu Li
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Gromov-Hausdorff Limits of Noncollapsed Kähler-Ricci Flows and the Geometry of Ricci Shrinkers
Topics (Non)collapsing, Limit spaces & RCD, Ricci solitons · Same author Yu Li · Shared terms “Ricci shrinkers”
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Heat kernel on Ricci shrinkers (II)
Topics Limit spaces & RCD, Ricci solitons · Same author Yu Li · Shared terms “Ricci shrinkers”
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On the geometry of asymptotically conical Ricci shrinkers (I): weighted analysis
Topics Limit spaces & RCD, Ricci solitons · Same author Yu Li · Shared terms “Ricci shrinkers”
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On the rigidity of Ricci shrinkers
Topics Limit spaces & RCD, Ricci solitons · Same author Yu Li · Shared terms “Ricci shrinkers”
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Singular sets in noncollapsed Ricci flow limit spaces
Topics (Non)collapsing, Limit spaces & RCD · Same author Yu Li · Shared terms “curvature bounds”
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
- 9B.3Collapsing and Noncollapsing
Injectivity radius bounds from volume, collapsing examples, and the definition Perelman needs.
- 12A.4κ-Noncollapsing
The theorem that excludes the cigar.
- 12A.8Local Noncollapsing from the Reduced Volume
Perelman's §§7.3 and 8: noncollapsing that needs only local curvature control, the small-and-large-vector split, the maximum principle for the reduced distance, and the form that survives surgery.