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

Maria Fernanda Elbert; Barbara Nelli; Walcy Santos

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

Differential Geometry 2015-08-13 v2

Authors: Maria Fernanda Elbert , Barbara Nelli , Walcy Santos

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.

Keywords

hypersurfaces hyperbolic space rotational hypersurfaces r-minimal hypersurfaces uniqueness theorem Schoen-type theorem higher order mean curvature

Cite

@article{arxiv.1503.07489,
  title  = {Hypersurfaces with H_{r+1}=0 in H x R},
  author = {Maria Fernanda Elbert and Barbara Nelli and Walcy Santos},
  journal= {arXiv preprint arXiv:1503.07489},
  year   = {2015}
}

Related papers

View all related →