A remark on the mean curvature of a graph-like hypersurface in hyperbolic space |
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Authors: | Zonglao Zhang |
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Institution: | Department of Mathematics, Wenzhou Normal College, Wenzhou, Zhejiang, 325027, PR China |
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Abstract: | In this paper we investigate the mean curvature H of a radial graph in hyperbolic space Hn+1. We obtain an integral inequality for H, and find that the lower limit of H at infinity is less than or equal to 1 and the upper limit of H at infinity is more than or equal to −1. As a byproduct we get a relation between the n-dimensional volume of a bounded domain in an n-dimensional hyperbolic space and the (n−1)-dimensional volume of its boundary. We also sharpen the main result of a paper by P.-A. Nitsche dealing with the existence and uniqueness of graph-like prescribed mean curvature hypersurfaces in hyperbolic space. |
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Keywords: | Mean curvature Graph-like hypersurface Hyperbolic space Partial differential equation |
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