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On the stability of spacelike hypersurfaces with higher order mean curvature in a de Sitter space

Shicheng Zhang
대한수학회 (The Korean Mathematical Society)|2014.09|대한수학회보 (Bulletin of the KMS)|제51권 제5호|pp. 1539-1549

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키워드

stabilityde Sitter spacespacelike hypersurfacehigher order mean curvature
주제분류수학

초록

The closed spacelike hypersurfaces with higher order mean curvature is discussed in a de Sitter space. The hypersurface is proved stable if and only if it is totally umbilical.

Abstract

The closed spacelike hypersurfaces with higher order mean curvature is discussed in a de Sitter space. The hypersurface is proved stable if and only if it is totally umbilical.

참고문헌 (13)

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  9. H. Cheng, "Stability and eigenvalue estimates of linear weingarten hyper-surfaces in a sphere", J. Math. Anal. Appl, 397(2), pp.658~670 (2013)
  10. S. Y. Cheng, "Hypersurfaces with constant scalar curvature", Math. Ann, 225(3), pp.195~204 (1977)
  11. X. Liu, "Stable space-like hypersurfaces in the de Sitter space", Arc. Math, 40(2), pp.111~117 (2004)
  12. M. A. Vel´asquez, "On the stability of hypersurfaces in space forms", J. Math. Anal. Appl, 406(1), pp.134~146 (2013)
  13. H. Rosenberg, "Hypersurfaces of constant curvature in space forms", Bull. Sci. Math, 117(2), pp.211~239 (1993)

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