具柱面奇点的泛型平均曲率流 I：法式与非退化性
微分几何
2025-08-27 v3 偏微分方程分析
动力系统
摘要
本文研究平均曲率流逼近柱面奇点时的动力学。我们证明了收敛到光滑广义柱面的重标度平均曲率流可在半径为 的球上写为柱面上的图，并给出了渐近性的一个法式。利用该法式，我们可定义柱面奇点的非退化性，并证明非退化柱面奇点在空间中是孤立的、具有平均凸邻域且为I型。
引用
@article{arxiv.2210.00419,
title = {Generic mean curvature flows with cylindrical singularities I: the normal forms and nondegeneracy},
author = {Ao Sun and Jinxin Xue},
journal= {arXiv preprint arXiv:2210.00419},
year = {2025}
}
备注
43 pages. We divide the original version into two parts, and this is the first part. The second part will be posted in the future. There are more details included, and for the references of later work, some new statements and arguments are added. Comments are welcome!