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Stable constant mean curvature hypersurfaces in ℝn+1 and ℍn+1(−1)

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Bulletin of the Brazilian Mathematical Society Aims and scope Submit manuscript

Abstract.

In this paper, we show that all complete stable hypersurfaces in ℝn+1(or ℍn+1 (-1)) (n = 3, 4, 5) with constant mean curvature H > 0 (or H > 1, respectively) and finite L 2 norm of traceless second fundamental form are compact geodesic spheres. Keywords: stable hypersurface, constant mean curvature, isometric immersion, Bernstein theorem.

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Authors and Affiliations

  1. Department of Mathematics, The Chinese University of Hong Kong, Shatin, New Territories, HONG KONG

    Leung-fu Cheung*

  2. Departamento de Geometria Insitituto de Matematica, Universidade Federal Fluminense—UFF Centro, 24020-140, Niterói, RJ, BRAZIL

    Detang Zhou**

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  1. Leung-fu Cheung*
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  2. Detang Zhou**
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Correspondence to Leung-fu Cheung*.

Additional information

*Supported by PolyU grant G-T575.

**Partially supported by CNPq of Brazil.

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Cheung*, Lf., Zhou**, D. Stable constant mean curvature hypersurfaces in ℝn+1 and ℍn+1(−1). Bull Braz Math Soc, New Series 36, 99–114 (2005). https://doi.org/10.1007/s00574-005-0030-6

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  • DOI: https://doi.org/10.1007/s00574-005-0030-6

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