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Graphs of Constant Mean Curvature in Hyperbolic Space

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Abstract

We study the problem of finding constant mean curvature graphsover a domain Ω of a totally geodesic hyperplane andan equidistant hypersurface Q of hyperbolic space. We findthe existence of graphs of constant mean curvature H overmean convex domains Ω ⊂ Q and with boundary∂Ω for −H ∂Ω < H ≤ |h|, where H ∂Ω> 0 is the mean curvature of the boundary ∂Ω. Here h is the mean curvature respectively of the geodesic hyperplane (h= 0) and of the equidistant hypersurface (0 < |h|< 1). The lower bound on H is optimal.

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  1. Departamento de Geometría y Topología, Universidad de Granada, 18071, Granada, Spain

    Rafael López

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  1. Rafael López
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López, R. Graphs of Constant Mean Curvature in Hyperbolic Space. Annals of Global Analysis and Geometry 20, 59–75 (2001). https://doi.org/10.1023/A:1010676217144

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