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Volume estimates for the singular sets of mean curvature flows

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arxiv 2504.09811 v1 pith:NQUHJ7EG submitted 2025-04-14 math.DG

Hanbing Fang , Yu Li This is my paper · ORCID
classification math.DG
keywords singularcurvatureestimatesflowsmeanvolumeclosedestablish
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abstract

In this paper, we establish uniform and sharp volume estimates for the singular set and the quantitative singular strata of mean curvature flows starting from a smooth, closed, mean-convex hypersurface in $\mathbb R^{n+1}$.

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  1. 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.

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