Hypersurfaces with H_{r+1}=0 in H x R

Abstract

We prove the existence of rotational hypersurfaces in ${\mathbb{H}}^n\times \mathbb{R}$ with $H_{r+1}=0$ and we classify them. Then we prove some uniqueness theorems for $r$-minimal hypersurfaces with a given (finite or asymptotic) boundary. In particular, we obtain a Schoen-type Theorem for two ended complete hypersurfaces.

References in corpus (1)

• Minimal hypersurfaces in $\HH^n \times \R$, total curvature and index