Existence of constant mean curvature graphs in hyperbolic space |
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Authors: | Rafael López Sebastián Montiel |
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Affiliation: | (1) Departamento de Geometría y Topología, Universidad de Granada. E-18071 Granada, Spain (e-mail: rcamino@ugr.es / smontiel@ugr.es) , ES |
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Abstract: | We give an existence result for constant mean curvature graphs in hyperbolic space . Let be a compact domain of a horosphere in whose boundary is mean convex, that is, its mean curvature (as a submanifold of the horosphere) is positive with respect to the inner orientation. If H is a number such that , then there exists a graph over with constant mean curvature H and boundary . Umbilical examples, when is a sphere, show that our hypothesis on H is the best possible. Received July 18, 1997 / Accepted April 24, 1998 |
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Keywords: | Mathematics Subject Classification (1991):53A10 53C42 |
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