Date of Award
Doctor of Philosophy
Alexandre S. Freire
Jochen Denzler, Mike Frazier, Seddik Djouadi
We investigate Inverse Mean Curvature Flow (IMCF) of non-compact hypersurfaces in hyperbolic space. Specifically, we look at bounded graphs over horospheres in Hyperbolic space and show long time existence of the flow as well as asymptotic convergence to horospheres. 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.
Allen, Brian Daniel, "Non-Compact Solutions to Inverse Mean Curvature Flow in Hyperbolic Space. " PhD diss., University of Tennessee, 2016.