ODE Maximum Principle at Infinity and Non-Compact Solutions of IMCF in Hyperbolic Space

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 ${\mathbb{H}}^{n+1}$ and show long time existence of the flow as well as asymptotic convergence to horospheres.

39 pages, substantial details added. arXiv admin note: text overlap with arXiv:1510.06670

References in corpus (1)

• Homothetic solitons for the inverse mean curvature flow

Cited by in corpus (3)

• Inverse Mean Curvature Flow and the Stability of the Positive Mass Theorem and Riemannian Penrose Inequality Under $L^2$ Metric Convergence
• Stability of the Positive Mass Theorem and Riemannian Penrose Inequality for Asymptotically Hyperbolic Manifolds Foliated by Inverse Mean Curvature Flow
• Long Time Existence of IMCF on Metrics Conformal to Warped Product Manifolds