Paper · Apr 8, 2019

Precise asymptotics near a generic singularity of mean curvature flow

Zhou Gang, Shengwen Wang

math.DGWider flowsarXiv:1904.04300v2
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Abstract

In the present paper we study a type of generic singularity of mean curvature flow modelled on the bubble-sheet , and we derive an asymptotic profile for a neighborhood of singularity.

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Submitted
Apr 8, 2019
Last revised
Oct 1, 2024 (v2)
Subjects
math.DG, math.AP

Comments: 12 pages, revised according to referee's suggestions

Mean curvature flowSingularities

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 2016, 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 On the dynamics of formation of generic singularities of mean curvature flow (Zhou Gang, 2017)1Gang 2017 On the mean convexity of a space-and-time neighborhood of generic singularities formed by mean curvature flow (Zhou Gang, 2018)2Gang 2018 Local Entropy and Generic Multiplicity One Singularities of Mean Curvature Flow of Surfaces (Ao Sun, 2018)7Sun 2018 Entropy and codimension bounds for generic singularities (Tobias Holck Colding and William P. Minicozzi, 2019)5Colding 2019 On the precise asymptotics of Type-IIb solutions to mean curvature flow (James Isenberg, Haotian Wu and Zhou Zhang, 2020)3Isenberg 2020 On the non-degenerate and degenerate generic singularities formed by mean curvature flow (Gang Zhou, 2021)6Zhou 2021 On the Stability of Cylindrical Singularities of the Mean Curvature Flow (Jingxuan Zhang, 2021)4Zhang 2021 Formation and structural stability of nondegenerate neckpinches (Kyeongsu Choi, Panagiota Daskalopoulos and Natasa Sesum, 2026)8Choi 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. On the dynamics of formation of generic singularities of mean curvature flow

    Zhou GangWider flows

    Topics Singularities · Same author Zhou Gang · Shared terms “generic singularities”, “neighborhood”

  2. On the mean convexity of a space-and-time neighborhood of generic singularities formed by mean curvature flow

    Zhou GangWider flows

    Topics Singularities · Same author Zhou Gang · Shared terms “generic singularities”, “neighborhood”

  3. On the precise asymptotics of Type-IIb solutions to mean curvature flow

    James Isenberg, Haotian Wu and Zhou ZhangWider flows

    Topics Singularities · Shared terms “precise asymptotics”

  4. On the Stability of Cylindrical Singularities of the Mean Curvature Flow

    Jingxuan ZhangWider flows

    Topics Singularities · Shared terms “precise asymptotics”

  5. Entropy and codimension bounds for generic singularities

    Tobias Holck Colding and William P. MinicozziWider flows

    Topics Singularities · Shared terms “generic singularities”

  6. On the non-degenerate and degenerate generic singularities formed by mean curvature flow

    Gang ZhouWider flows

    Topics Singularities · Shared terms “generic singularities”, “neighborhood”, “modelled”

  7. Local Entropy and Generic Multiplicity One Singularities of Mean Curvature Flow of Surfaces

    Ao SunWider flows

    Topics Singularities · Shared terms “generic singularities”

  8. Formation and structural stability of nondegenerate neckpinches

    Kyeongsu Choi, Panagiota Daskalopoulos and Natasa SesumWider flows

    Topics Singularities · Shared terms “precise asymptotics”

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 in the L² sense. Start with: Flow by mean curvature of convex surfaces into spheres (Huisken, 1984) Singularities On a closed manifold the flow can stop in finite time: curvature blows up, 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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    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.

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

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