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 \(\mathbb{H}^{n+1}\) 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.