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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Received: 9 March 2001
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Nitsche, PA. Existence of prescribed mean curvature graphs in hyperbolic space. Manuscripta Math. 108, 349–367 (2002). https://doi.org/10.1007/s002290200267
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DOI: https://doi.org/10.1007/s002290200267