Acta mathematica scientia,Series B ›› 2013, Vol. 33 ›› Issue (3): 830-838.doi: 10.1016/S0252-9602(13)60042-9

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STABILITY OF CONSTANT MEAN CURVATURE HYPERSURFACES OF REVOLUTION IN HYPERBOLIC SPACE

Mohamed JLELI   

  1. Department of Mathematics, King Saud Unibersity, Saudi Arabia
  • Received:2011-12-30 Revised:2012-05-24 Online:2013-05-20 Published:2013-05-20
  • Supported by:

    This work is supported by the King Saud University D.S.F.P program.

Abstract:

In this article, by solving a nonlinear differential equation, we prove the existence of a one parameter family of constant mean curvature hypersurfaces in the hyperbolic space with two ends. Then, we study the stability of these hypersurfaces.

Key words: Hypersurface, hyperbolic space, mean curvature

CLC Number: 

  • 53C42
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