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Mean curvature flow with generic low-entropy initial data II

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arxiv 2309.03856 v2 pith:ZD6PDIBF submitted 2023-09-07 math.DG

Otis Chodosh , Christos Mantoulidis , Felix Schulze This is my paper · ORCID
classification math.DG
keywords mathbbgenericcurvatureentropyflowmeancloseddata
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abstract

We prove that the mean curvature flow of a generic closed embedded hypersurface in $\mathbb{R}^4$ or $\mathbb{R}^5$ with entropy $\leq 2$, or with entropy $\leq \lambda(\mathbb{S}^1)$ if in $\mathbb{R}^6$, encounters only generic singularities.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Generic regularity for minimizing hypersurfaces in dimension 11

    math.DG 2025-06 conditional novelty 8.0 of 10

    Area-minimizing hypersurfaces are generically smooth in ambient dimension 11 after a C-infinity-small perturbation of the boundary or metric, and in dimensions 12 and up the singular set has dimension at most n-10-epsilon_n.

  2. Regularity of cylindrical singular sets of mean curvature flow

    math.DG 2025-09 conditional novelty 7.0 of 10

    Degenerate cylindrical singular sets of mean curvature flow are locally contained in C^{2,α} submanifolds, with curvature determined by the flow's asymptotic profile.

  3. Passing through nondegenerate singularities in mean curvature flows

    math.DG 2025-01 conditional novelty 7.0 of 10

    Mean curvature flows through nondegenerate cylindrical singularities undergo an isolated, graphical surgery event whose topology change equals an (n-k)-surgery, matching Morse level sets.

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