Paper · Nov 19, 2025

Decay order bound for mean curvature flow near compact singularities

Sourav Ghosh

math.DGWider flowsarXiv:2511.15297
PDF Abstract page

As on arXiv

Abstract

We consider the rescaled flow associated with a mean curvature flow that develops a compact singularity of multiplicity one. We prove that the "decay order" of such a rescaled flow is uniformly bounded. As a consequence, we prove a unique continuation result.

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 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 Type II smoothing in mean curvature flow (Sigurd Angenent, Panagiota Daskalopoulos and Natasa Sesum, 2021)7Angenent 2021 On the Stability of Cylindrical Singularities of the Mean Curvature Flow (Jingxuan Zhang, 2021)8Zhang 2021 Passing through nondegenerate singularities in mean curvature flows (Ao Sun, Zhihan Wang and Jinxin Xue, 2025)6Sun 2025 How close is too close for singular mean curvature flows? (Joshua Daniels-Holgate and Or Hershkovits, 2025)4Daniels-Holg 2025 Lagrangian mean curvature flow of surfaces with mean curvature bound (Sourav Ghosh, 2025)1Ghosh 2025 Cylindrical tangent flows in mean curvature flow (Sourav Ghosh, 2025)2Ghosh 2025 On the rate of convergence of cylindrical singularity in mean curvature flow (Yiqi Huang and Xinrui Zhao, 2025)5Huang 2025 Uniqueness of tangent flows in free boundary flow (Sourav Ghosh, 2026)3Ghosh 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Lagrangian mean curvature flow of surfaces with mean curvature bound

    Sourav GhoshWider flows PDF

    Topics Singularities · Same author Sourav Ghosh · Shared terms “uniformly bounded”

  2. Cylindrical tangent flows in mean curvature flow

    Sourav GhoshWider flows PDF

    Topics Singularities · Same author Sourav Ghosh

  3. Uniqueness of tangent flows in free boundary flow

    Sourav GhoshWider flows PDF

    Topics Singularities · Same author Sourav Ghosh

  4. How close is too close for singular mean curvature flows?

    Joshua Daniels-Holgate and Or HershkovitsWider flows PDF

    Topics Singularities · Shared terms “compact singularity”, “multiplicity”

  5. On the rate of convergence of cylindrical singularity in mean curvature flow

    Yiqi Huang and Xinrui ZhaoWider flows PDF

    Topics Singularities · Shared terms “unique continuation”, “rescaled”

  6. Passing through nondegenerate singularities in mean curvature flows

    Ao Sun, Zhihan Wang and Jinxin XueWider flows PDF

    Topics Singularities · Shared terms “decay order”

  7. Type II smoothing in mean curvature flow

    Sigurd Angenent, Panagiota Daskalopoulos and Natasa SesumWider flows PDF

    Topics Singularities · Shared terms “uniformly bounded”, “continuation”

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

    Jingxuan ZhangWider flows PDF

    Topics Singularities · Shared terms “rescaled”

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

  1. 6A.13
    Self-Similar Variables and MonotonicityBook 6A · The Heat Equation and Its Relatives

    Changing variables so that self-similar solutions stand still: convergence to the Gaussian, Giga–Kohn blow-up, Gaussian-weighted monotonicity formulas, frequency functions, and the blow-up logic of Huisken, Struwe and Perelman.

  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.