Mean curvature flow converging to an minimizing cone and its Hardt-Simon foliation

Jiuzhou Huang

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arXiv · 2510.11430

Mean curvature flow converging to an minimizing cone and its Hardt-Simon foliation

Jiuzhou Huang

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Abstract

In this paper, we construct a family of mean curvature flow which converges to an area minimizing, strictly stable hypercone $\mC$ after type I rescaling, and converges to the Hardt-Simon foliation of the cone after a type II rescaling provided the cone satisfies some technique conditions. The difference from Vel\'azquez's previous results is that we drop the symmetry condition on the cone.

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Jiuzhou Huang. 2025-10-13. Mean curvature flow converging to an minimizing cone and its Hardt-Simon foliation. https://arxiv.org/abs/2510.11430

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