English

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

Differential Geometry 2025-10-14 v1

Abstract

In this paper, we construct a family of mean curvature flow which converges to an area minimizing, strictly stable hypercone \mC\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.

Keywords

Cite

@article{arxiv.2510.11430,
  title  = {Mean curvature flow converging to an minimizing cone and its Hardt-Simon foliation},
  author = {Jiuzhou Huang},
  journal= {arXiv preprint arXiv:2510.11430},
  year   = {2025}
}