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On Alexandrov-Bernstein theorems in hyperbolic space. (English) Zbl 0534.53049

The authors consider complete properly embedded hypersurfaces of constant mean curvature in hyperbolic n-space. Among them they characterize distance ”spheres” 1) around a point, 2) around a geodesic hypersurface and 3) horospheres by the behaviour of their asymptotic boundary.
Reviewer: D.Ferus

MSC:

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53A35 Non-Euclidean differential geometry
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References:

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