Paper · Sep 7, 2023

Mean curvature flow with generic low-entropy initial data II

Otis Chodosh, Christos Mantoulidis, Felix Schulze

math.DGWider flowsarXiv:2309.03856v2
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Abstract

We prove that the mean curvature flow of a generic closed embedded hypersurface in or with entropy , or with entropy if in , encounters only generic singularities.

Comments: Final version, to appear in Duke Math. J

Mean curvature flowSingularities

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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.

Connected papers This paper in the centre and the 8 papers closest to it around it, in date order clockwise from the top. The closer a paper sits to the centre, the stronger the connection. This paper Mean curvature flow with generic initial data II (Otis Chodosh, Kyeongsu Choi and Felix Schulze, 2023)1Chodosh 2023 Singularities of low entropy high codimension curve shortening flow (Florian Litzinger, 2023)4Litzinger 2023 Mean Curvature Flow from Conical Singularities (Otis Chodosh, J. M. Daniels-Holgate and Felix Schulze, 2023)3Chodosh 2023 Revisiting generic mean curvature flow in ℝ³ (Otis Chodosh, Kyeongsu Choi, Christos Mantoulidis et al., 2024)2Chodosh 2024 Backwards uniqueness for Mean curvature flow with asymptotically conical singularities (J. M. Daniels-Holgate and Or Hershkovits, 2025)8Daniels-Holg 2025 Morse resolution of mean curvature flows with cylindrical singularities (Richard H. Bamler, Felix Schulze and Lu Wang, 2026)5Bamler 2026 Generic mean curvature flow has finitely many singularities (J. M. Daniels-Holgate, Or Hershkovits and Gábor Székelyhidi, 2026)6Daniels-Holg 2026 Compact Mean Curvature Flows from Non-Compact Initial Data (Theodora Bourni, Nathan Burns and Marcus Flook, 2026)7Bourni 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Mean curvature flow with generic initial data II

    Otis Chodosh, Kyeongsu Choi and Felix SchulzeWider flows PDF

    Topics Singularities · Same authors Otis Chodosh, Felix Schulze · Shared terms “initial data”, “generic closed”

  2. Revisiting generic mean curvature flow in

    Otis Chodosh, Kyeongsu Choi, Christos Mantoulidis et al.Wider flows PDF

    Topics Singularities · Same authors Otis Chodosh, Christos Mantoulidis, Felix Schulze

  3. Mean Curvature Flow from Conical Singularities

    Otis Chodosh, J. M. Daniels-Holgate and Felix SchulzeWider flows PDF

    Topics Singularities · Same authors Otis Chodosh, Felix Schulze

  4. Singularities of low entropy high codimension curve shortening flow

    Florian LitzingerWider flows PDF

    Topics Singularities · Shared terms “low entropy”

  5. Morse resolution of mean curvature flows with cylindrical singularities

    Richard H. Bamler, Felix Schulze and Lu WangWider flows PDF

    Topics Singularities · Same author Felix Schulze

  6. Generic mean curvature flow has finitely many singularities

    J. M. Daniels-Holgate, Or Hershkovits and Gábor SzékelyhidiWider flows PDF

    Topics Singularities · Shared terms “encounter”

  7. Compact Mean Curvature Flows from Non-Compact Initial Data

    Theodora Bourni, Nathan Burns and Marcus FlookWider flows PDF

    Topics Singularities · Shared terms “initial data”

  8. Backwards uniqueness for Mean curvature flow with asymptotically conical singularities

    J. M. Daniels-Holgate and Or HershkovitsWider flows PDF

    Topics Singularities · Shared terms “low entropy”, “encounter”

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.

Mean curvature flow Wider flows A hypersurface moves in the direction of its mean curvature vector, which decreases area as fast as possible. Start with: Flow by mean curvature of convex surfaces into spheres (Huisken, 1984) Singularities On a closed manifold the flow usually cannot run forever: curvature blows up in finite time, often because a neck pinches off. Start with: The formations of singularities in the Ricci Flow (Hamilton, 1993)

In the guidebook

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  2. 6C.8
    Monotonicity, ε-Regularity and Tangent ConesBook 6C · Nonlinear PDE: Variational and Geometric Methods

    Monotonicity formulas for minimal surfaces and harmonic maps, small energy implies smoothness, bubble trees, tangent cones and dimension reduction, with soap films, liquid crystals and pseudolocality.

  3. 11B.4
    Blow-Ups, Blow-Downs and Splitting at InfinityBook 11B · Solitons, Compactness and Singularities

    Limits of rescaled manifolds and flows: why blow-up limits are nonnegatively curved, what blow-downs see, and how lines appear at infinity.