English

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

Differential Geometry 2018-04-16 v3

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

Keywords

Cite

@article{arxiv.1610.01211,
  title  = {ODE Maximum Principle at Infinity and Non-Compact Solutions of IMCF in Hyperbolic Space},
  author = {Brian Allen},
  journal= {arXiv preprint arXiv:1610.01211},
  year   = {2018}
}

Comments

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

R2 v1 2026-06-22T16:10:47.785Z