Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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STABLE MINIMAL HYPERSURFACES IN THE HYPERBOLIC SPACE

  • Seo, Keom-Kyo (DEPARTMENT OF MATHEMATICS SOOKMYUNG WOMEN'S UNIVERSITY)
  • Received : 2009.09.02
  • Published : 2011.03.01
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Abstract

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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References

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