# Examples of $H$-hypersurfaces in $H^n \times R$ and geometric applications

Abstract : 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 $H^n \times R$. For $n>2$ we obtain a complete embedded translation hypersurface generated by a compact, simple, strictly convex curve. When $0 < H < \frac{n-1}{n}$ 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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Article dans une revue
Matemática Contemporânea, Sociedade Brasileira de Matemática, 2008, 34 (2008), pp.19-51

https://hal.archives-ouvertes.fr/hal-00360077
Contributeur : Pierre Bérard <>
Soumis le : lundi 4 mai 2009 - 17:22:21
Dernière modification le : lundi 2 novembre 2015 - 16:56:06
Document(s) archivé(s) le : mercredi 22 septembre 2010 - 12:39:10

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• HAL Id : hal-00360077, version 2
• ARXIV : 0902.1623

### Citation

Pierre Bérard, Ricardo Sa Earp. Examples of $H$-hypersurfaces in $H^n \times R$ and geometric applications. Matemática Contemporânea, Sociedade Brasileira de Matemática, 2008, 34 (2008), pp.19-51. <hal-00360077v2>

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