zbMATH — the first resource for mathematics

Constant mean curvature surfaces in hyperbolic space. (English) Zbl 0757.53032
The authors study the global geometry of complete, proper surfaces in hyperbolic \((n+1)\)-space with constant curvature \(>n\). Main results are, that such are never closed surfaces with only one puncture. If they have two punctures that are Delaunay cylinders, and if they have 3 punctures they remain a bounded distance from a geodesic plane. As in the Euclidean case, annular ends converge to Delaunay surfaces.
Reviewer: D.Ferus (Berlin)

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