, Volume 13, Issue 1, pp 23-30

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.

Communicated by D. Ferus