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arXiv · 1610.01211

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

Brian Allen
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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.

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Brian Allen. 2016-10-04. ODE Maximum Principle at Infinity and Non-Compact Solutions of IMCF in Hyperbolic Space. https://arxiv.org/abs/1610.01211

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