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

Authors: Yongheng Han

I find that there is a mistake in the proof of Theorem 2.2, I give a new proof in this version

Abstract: We study the multiplicity of the singularity 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 $\mathbb{R}^{n+1}$.

Submitted to arXiv on 09 Jan. 2025

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