双曲空间中非紧致反平均曲率流的长时间存在
微分几何
2016-10-18 v3
摘要
我们研究双曲空间中非紧致超曲面的反平均曲率流（IMCF）。具体地，我们考察中极限球上的有界图，并证明该流的长时间存在性。在此过程中，获得了许多重要的局部估计与全局估计。此外，我们为IMCF发展了一族有用的截断函数，以及非紧致无穷远处的ODE最大值原理，这些是整个文档中使用的基本工具。
引用
@article{arxiv.1510.06670,
title = {Long Time Existence of Non-Compact Inverse Mean Curvature Flow in Hyperbolic Space},
author = {Brian Allen},
journal= {arXiv preprint arXiv:1510.06670},
year = {2016}
}
备注
This paper has been withdrawn by the author due to technical issues with the interior estimates of the second fundamental form as well as interior estimates of lower bounds on the mean curvature. See my latest submission entitled, "ODE Maximum Principle at Infinity and Non-Compact Solutions of Inverse Mean Curvature Flow in Hyperbolic Space" arXiv:1610.01211 for correct results