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.

Matemática Contemporânea 34, 2008 (2009) to appear

References in corpus (2)

• Minimal hypersurfaces in $\HH^n \times \R$, total curvature and index
• Vertical Ends of Constant Mean Curvature H=1/2 in H^2\times R