Some remarks on compact constant mean curvature hypersurfaces in a halfspace of \(\mathbb{H}^{n+1}\). (English) Zbl 0981.53049

Nelli, Barbara; Semmler, Beate

J. Geom. 64, No. 1-2, 128-140 (1999).

The authors give a theorem (see the abstract of the paper for a complete statement of it) for hypersurfaces of constant mean curvature in a halfspace of hyperbolic space \(\mathbb H ^{n+1}\). They consider embedded compact hypersurfaces \(M\) with boundary \(\partial M\) in the boundary geodesic hyperplane \(P\) of the halfspace and with non-zero mean curvature. They also prove a result about the topology of such hypersurfaces.

Reviewer: Ildefonso Castro Lopez (Jaen)

MSC:

53C42	Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53A10	Minimal surfaces in differential geometry, surfaces with prescribed mean curvature

Keywords:

constant mean curvature; large hypersurfaces; Alexandrov reflection technique

References:

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