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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)

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