Singularities of mean curvature flow with bounded mean curvature and Morse index

Yongheng Han

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arXiv · 2501.05489

Singularities of mean curvature flow with bounded mean curvature and Morse index

Yongheng Han

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Abstract

We study the multiplicity of the singularities of mean curvature flow with bounded mean curvature and Morse index. For $3\leq n\leq 6$, we show that either the mean curvature or the Morse index blows up at the first singular time for a closed smooth embedded mean curvature flow in $\mathbb{R}^{n+1}$.

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Yongheng Han. 2025-01-09. Singularities of mean curvature flow with bounded mean curvature and Morse index. https://arxiv.org/abs/2501.05489

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