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

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

2009-02-10

arxiv.org/abs/0902.1623v2

Matem\'atica contempor\^anea 34, 2008 (2008) 19-51

Mathematics

Differential Geometry

Matem\'atica Contempor\^anea 34, 2008 (2009) to appear

Scientific paper

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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