ODE Maximum Principle at Infinity and Non-Compact Solutions of IMCF in Hyperbolic Space
Differential Geometry
2018-04-16 v3
Abstract
In this work we extend the ODE Maximum principle of Hamilton to non-compact hypersurfaces using the Omari-Yau maximum principle at infinity. As an application of this result, 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 as well as asymptotic convergence to horospheres.
Cite
@article{arxiv.1610.01211,
title = {ODE Maximum Principle at Infinity and Non-Compact Solutions of IMCF in Hyperbolic Space},
author = {Brian Allen},
journal= {arXiv preprint arXiv:1610.01211},
year = {2018}
}
Comments
39 pages, substantial details added. arXiv admin note: text overlap with arXiv:1510.06670