Non-Compact Solutions to Inverse Mean Curvature Flow in Hyperbolic Space

Author

Brian Daniel Allen, University of Tennessee - KnoxvilleFollow

Date of Award

5-2016

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

Alexandre S. Freire

Committee Members

Jochen Denzler, Mike Frazier, Seddik Djouadi

Abstract

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.

Recommended Citation

Allen, Brian Daniel, "Non-Compact Solutions to Inverse Mean Curvature Flow in Hyperbolic Space. " PhD diss., University of Tennessee, 2016.
https://trace.tennessee.edu/utk_graddiss/3675