由 $-\infty$ 处切流给出的古代平均曲率流的余维数界与刚性
微分几何
2021-10-27 v2 偏微分方程分析
摘要
受一类显式紧致古代曲线缩短流的极限行为启发，我们证明了古代平均曲率流由其 处切流给出的余维数界，推广了[CM19b]中关于柱面的定理。在 重圆的情况下，我们应用该界证明了一个强刚性定理。进一步，我们拓展了这一范式，表明在充分快速收敛的假设下，一个紧致古代平均曲率流与其 处切流恒等。
引用
@article{arxiv.1909.02535,
title = {Codimension Bounds and Rigidity of Ancient Mean Curvature Flows by the Tangent Flow at $-\infty$},
author = {Douglas Stryker and Ao Sun},
journal= {arXiv preprint arXiv:1909.02535},
year = {2021}
}
备注
17 pages. Modify the paper according to the referees' suggestion. In particular we remove Theorem 1.3 in the previous version, where there is a gap in the proof. Accepted by Communications in Contemporary Mathematics. arXiv admin note: text overlap with arXiv:1908.02688