Long Time Existence of Non-Compact Inverse Mean Curvature Flow in Hyperbolic Space
Abstract
We investigate Inverse Mean Curvature Flow (IMCF) of non-compact hypersurfaces in hyperbolic space. Specifically, we look at bounded graphs over horospheres in and show long time existence of the flow. Along the way many important local estimates as well as global estimates are obtained. In addition, we develop a useful family of cutoff functions for IMCF as well as a non-compact ODE maximum principle at infinity which are integral tools used throughout the document.
Keywords
Cite
@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}
}
Comments
This paper has been withdrawn by the author due to technical issues with the interior estimates of the second fundamental form as well as interior estimates of lower bounds on the mean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