As on arXiv
Abstract
We study tangent flows of noncollapsed Ricci flow limit spaces in the sense of Fang-Li. We prove that the regular part of every negative time slice is geodesically convex: any minimizing geodesic that meets the regular part has its entire interior contained in it. We also identify each negative time slice with the metric completion of its regular Riemannian part, thereby identifying the negative-time tangent flow with its associated metric soliton.
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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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On the structure of noncollapsed Ricci flow limit spaces
Topics (Non)collapsing · Same author Yu Li · Shared terms “noncollapsed Ricci”, “flow limit”, “limit space”
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Singular sets in noncollapsed Ricci flow limit spaces
Topics (Non)collapsing, Singularities · Same author Yu Li · Shared terms “noncollapsed Ricci”, “flow limit”, “limit space”
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Gromov-Hausdorff convergence of time-slices of singular Ricci flows in dimension three
Topics (Non)collapsing · Same author Yu Li · Shared terms “time slice”, “regular part”, “noncollapsed Ricci”
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Gromov-Hausdorff Limits of Noncollapsed Kähler-Ricci Flows and the Geometry of Ricci Shrinkers
Topics (Non)collapsing, Singularities · Same author Yu Li · Shared terms “noncollapsed”, “regular part”, “time slice”
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On noncollapsed -limit metric solitons
Topics (Non)collapsing, Singularities · Shared terms “noncollapsed”
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On the fundamental group of non-collapsed ancient Ricci flows
Topics (Non)collapsing, Singularities · Shared terms “regular part”, “tangent flow”
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Ancient Ricci flows with nonnegative Ricci curvature
Topics (Non)collapsing, Singularities · Shared terms “tangent flow”, “noncollapsed”
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Non-collapsing of Ricci shrinkers with bounded curvature
Topics (Non)collapsing · Same author Yu Li
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.