Stable minimal hypersurfaces in the hyperbolic space
Differential Geometry
2010-02-23 v1
Abstract
In this paper we give an upper bound of the first eigenvalue of the Laplace operator on a complete stable minimal hypersurface in the hyperbolic space which has finite -norm of the second fundamental form on . We provide some sufficient conditions for minimal hypersurface of the hyperbolic space to be stable. We also describe stability of catenoids and helicoids in the hyperbolic space. In particular, it is shown that there exists a family of stable higher-dimensional catenoids in the hyperbolic space.
Cite
@article{arxiv.1002.3898,
title = {Stable minimal hypersurfaces in the hyperbolic space},
author = {Keomkyo Seo},
journal= {arXiv preprint arXiv:1002.3898},
year = {2010}
}
Comments
This article is to appear in J. Korean Math. Soc. in 2010