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Some remarks on embedded hypersurfaces in hyperbolic space of constant curvature and spherical boundary

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Abstract

We consider embedded hypersurfacesM in hyperbolic space with compact boundaryC and somer th mean curvature functionH r a positive constant. We investigate when symmetries ofC are symmetries ofM. We prove that if 0≤H r≤1 andC is a sphere thenM is a part of an equidistant sphere. Forr=1 (H 1 is the mean curvature) we obtain results whenC is convex.

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Authors and Affiliations

  1. Dipartimento di Matematica, via Buonarroti 2, 56127, Pisa, Italy

    Barbara Nelli

  2. Département de Mathématiques, Université de Paris VII, 2, Place Jussieu, 75251, Paris, France

    Harold Rosenberg

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  1. Barbara Nelli
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  2. Harold Rosenberg
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Communicated by D. Ferus

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Nelli, B., Rosenberg, H. Some remarks on embedded hypersurfaces in hyperbolic space of constant curvature and spherical boundary. Ann Glob Anal Geom 13, 23–30 (1995). https://doi.org/10.1007/BF00774564

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  • DOI: https://doi.org/10.1007/BF00774564

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