Constant mean curvature hypersurfaces in $\mathbb H^n\times\mathbb R$ with small planar boundary

Barbara Nelli; Giuseppe Pipoli

Constant mean curvature hypersurfaces in $\mathbb H^n\times\mathbb R$ with small planar boundary

Differential Geometry 2021-10-11 v1

Authors: Barbara Nelli , Giuseppe Pipoli

Abstract

We show that constant mean curvature hypersurfaces in $\mathbb H^n\times\mathbb R$ , with small and pinched boundary contained in a horizontal slice $P$ are topological disks, provided they are contained in one of the two halfspaces determined by $P$ . This is the analogous in $\mathbb H^n\times\mathbb R$ of a result in $\mathbb R^3$ by A. Ros and H. Rosenberg.

Keywords

constant mean curvature hypersurfaces hyperbolic space topological disk pinched boundary

Cite

@article{arxiv.2110.03985,
  title  = {Constant mean curvature hypersurfaces in $\mathbb H^n\times\mathbb R$ with small planar boundary},
  author = {Barbara Nelli and Giuseppe Pipoli},
  journal= {arXiv preprint arXiv:2110.03985},
  year   = {2021}
}

Comments

18 pages, 3 figures, comments are welcome

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