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Mean curvature flow with generic initial data II

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arxiv 2302.08409 v1 pith:RXFRCWN6 submitted 2023-02-16 math.DG math.AP

Otis Chodosh , Kyeongsu Choi , Felix Schulze This is my paper · ORCID
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abstract

We show that the mean curvature flow of a generic closed surface in $\mathbb{R}^3$ avoids multiplicity one tangent flows that are not round spheres/cylinders. In particular, we show that any non-cylindrical self-shrinker with a cylindrical end cannot arise generically.

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Cited by 4 Pith papers

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

  1. Classification of ancient noncollapsed flows in $\mathbb{R}^4$

    math.DG 2024-12 accept novelty 8.0 of 10

    Every ancient noncollapsed mean curvature flow in R^4 is one of the known shrinkers, bowls, ovals, or Hoffman-Ilmanen-Martin-White translators.

  2. Type-I Blowup Solutions for Yang-Mills Flow

    math.DG 2024-11 conditional novelty 8.0 of 10

    For 5 to 9 dimensions, an infinite-dimensional family of Yang-Mills flow solutions is constructed that converge, modulo gauge, to the homothetically shrinking soliton W, including asymmetric Type-I blowups.

  3. Ancient mean curvature flow asymptotic to Simons cone

    math.DG 2026-08 accept novelty 7.0 of 10

    Ancient mean curvature flows asymptotic to the Simons cone from one side have unique asymptotics; adding mean convexity forces them to be stationary Hardt-Simon leaves.

  4. 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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