Existence of prescribed mean curvature graphs in hyperbolic space |
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Authors: | Pál-Andrej Nitsche |
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Affiliation: | (1) Seminar für Angewandte Mathematik, HG G 54.1, ETH Zentrum, CH-8092 Zürich, Switzerland. e-mail: andrej.nitsche@math.ethz.ch, CH |
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Abstract: | In this paper we are concerned with questions of existence and uniqueness of graph-like prescribed mean curvature hypersurfaces in hyperbolic space ?n+1. In the half-space setting, we will study radial graphs over the totally geodesic hypersurface . We prove the following existence result: Let be a bounded domain of class and let . If everywhere on , where denotes the hyperbolic mean curvature of the cylinder over , then for every there is a unique graph over with mean curvature attaining the boundary values on . Further we show the existence of smooth boundary data such that no solution exists in case of for some under the assumption that has a sign. |
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