Singularities of Mean Curvature Flow with Bounded Total Curvature

Yongheng Han; Zhen Wang

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arXiv · 2610.18197

Singularities of Mean Curvature Flow with Bounded Total Curvature

Yongheng Han·Zhen Wang

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Abstract

We prove that every tangent flow at the first singular time of a smooth, closed, embedded mean curvature flow has smooth support, provided that the total curvature satisfies $\sup_{t\in[0,T)}\int_{M_t}|A|^n\,dμ_t<\infty$. This extends Ilmanen's smoothness result for tangent flows to higher dimensions.

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BibTeX RIS

Yongheng Han, Zhen Wang. 2026-10-13. Singularities of Mean Curvature Flow with Bounded Total Curvature. https://arxiv.org/abs/2610.18197

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