J. Korean Math. Soc. 2011; 48(2): 253-266
Printed March 1, 2011
https://doi.org/10.4134/JKMS.2011.48.2.253
Copyright © The Korean Mathematical Society.
Keomkyo Seo
Sookmyung Women's University
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.
Keywords: stable minimal hypersurface, hyperbolic space, first eigenvalue
MSC numbers: 53C40, 53C42
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