Stable minimal hypersurfaces in the hyperbolic space

Details Stable minimal hypersurfaces in the hyperbolic space Stable minimal hypersurfaces in the hyperbolic space

2010-02-20

arxiv.org/abs/1002.3898v1

Mathematics

Differential Geometry

This article is to appear in J. Korean Math. Soc. in 2010

Scientific paper

In this paper we give an upper bound of the first eigenvalue of the Laplace operator on a complete stable minimal hypersurface $M$ in the hyperbolic space which has finite $L^2$-norm of the second fundamental form on $M$. 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.

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