×

zbMATH — the first resource for mathematics

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.

MSC:
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Alexandrov, A.D.: Uniqueness theorems for surfaces in the large. V. Vestnik Leningrad Univ., 13 No. 19 A.M.S. (Series 2)21 (1958) 412-416.
[2] De Miranda Gomez, J.: Sobre hipersuperficies com curvatura media constante no espaco hiperbolico. PhD thesis, IMPA (1985).
[3] Gilbarg, D. andTrudinger, N.S.: Elliptic Partial Differential Equations of Second Order. Springer-Verlag (1983). · Zbl 0562.35001
[4] Korevaar, N. andKusner, R. andMeeks III,W.H. andSolomon, B.: Constant mean curvature surfaces in hyperbolic space. American Journal of Mathematics114 (1992) 1-43. · Zbl 0757.53032 · doi:10.2307/2374738
[5] Ros, A. andRosenberg, H.: Constant mean curvature surfaces in a half-space of ?3 with boundary in the boundary of the half-space. To appear in Journal of Differential Geometry (1997).
[6] Semmler, B.: Blow up theorems for compact constant mean curvature surfaces. Preprint (1997).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.