EXAMPLES OF H - HYPERSURFACES IN H n × R AND GEOMETRIC APPLICATIONS
نویسندگان
چکیده
In this paper we describe all rotation H-hypersurfaces in Hn × R and use them as barriers to prove existence and characterization of certain vertical H-graphs and to give symmetry and uniqueness results for compact H-hypersurfaces whose boundary is one or two parallel submanifolds in slices. We also describe examples of translation H-hypersurfaces in Hn × R. For n > 2 we obtain a complete embedded translation hypersurface generated by a compact, simple, strictly convex curve. When 0 < H < n−1 n we obtain a complete non-entire vertical graph over the non-mean convex domain bounded by an equidistant hypersurface taking infinite boundary value data and infinite asymptotic boundary value data.
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Fe b 20 09 Examples of H - hypersurfaces in H n × R and geometric applications
In this paper we describe all rotation H-hypersurfaces in Hn×R and use them as barriers to prove existence and characterization of certain vertical H-graphs and to give symmetry and uniqueness results for compact H-hypersurfaces whose boundary is one or two parallel submanifolds in slices. We also describe examples of translation H-hypersurfaces in Hn × R. In particular, for H < n−1 n , we obta...
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