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

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