A Mountain-pass Theorem in Hyperbolic Space and its Application
Differential Geometry
2022-06-28 v1
Abstract
We develop a min-max theory for certain complete minimal hypersurfaces in hyperbolic space. In particular, we show that given two strictly stable minimal hypersurfaces that are both asymptotic to the same ideal boundary, there is a new one trapped between the two. As an application, we show that under a low entropy condition, all the minimal hypersurfaces asymptotic to the same ideal boundary are isotopic.
Cite
@article{arxiv.2206.13145,
title = {A Mountain-pass Theorem in Hyperbolic Space and its Application},
author = {Junfu Yao},
journal= {arXiv preprint arXiv:2206.13145},
year = {2022}
}