Examples of $H$-hypersurfaces in $H^n \times R$ and geometric applications
Résumé
In this paper we describe all rotation $H$-hypersurfaces in $H^n \times R$ 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 $H^n \times R$. In particular, for $H < \frac{n-1}{n}$, we obtain a complete non-entire vertical graph taking infinite boundary value data.
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