具有柱状奇点的平均曲率流的Morse解消
Morse resolution of mean curvature flows with cylindrical singularities
浏览论文内容
中文总结 AI 辅助
本文证明具有重数为一柱状切流的紧致平均曲率流存在光滑Morse解消，该解消在奇点集外与时空轨迹一致，临界点指标符合预期，无需非退化或孤立假设，平均凸情形通过对全局到达函数光滑化得到。
中文摘要 AI 辅助
我们证明，一个奇点具有重数为一的柱状切流的紧致平均曲率流，允许一个光滑的Morse解消。该解消在其奇点集的任何给定邻域之外与时空轨迹一致，且其所有临界点具有预期的指标。无需非退化性或孤立性假设。在平均凸情形下，该结果通过对全局到达函数进行光滑化而得出。
英文摘要
We show that a compact mean curvature flow whose singularities have multiplicity-one cylindrical tangent flows admits a smooth Morse resolution. The resolution agrees with the spacetime track outside any prescribed neighborhood of its singular set and all its critical points have the expected index. No nondegeneracy or isolatedness assumption is required. In the mean-convex case the result follows by smoothing the global arrival function.
发表机构
- Department of Mathematics, UC Berkeley（加州大学伯克利分校数学系）
- Mathematics Institute, University of Warwick（华威大学数学研究所）
- Department of Mathematics, Yale University（耶鲁大学数学系）
机构由 AI 辅助整理，请以论文原文为准。
