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

Pierre Bérard (1) , Ricardo Sa Earp (2)

1 IF - Institut Fourier
2 Departamento de Matematica

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.

Mots clés: Constant mean curvature; Rotation and Translation hypersurfaces; Vertical graphs; Dirichlet problem

Domaines: Géométrie différentielle [math.DG]

Pierre Bérard, Ricardo Sa Earp. Examples of $H$-hypersurfaces in $H^n \times R$ and geometric applications. 2009. ⟨hal-00360077v1⟩