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

2025/01/09 by Yongheng Han, Han, Yongheng
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2501.05489

Abstract

We study the multiplicity of the singularities of mean curvature flow with bounded mean curvature and Morse index. For 3≤ n≤ 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 ℝⁿ⁺¹.

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