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

Barbara Nelli; Giuseppe Pipoli

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arXiv · 2110.03985

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

Barbara Nelli·Giuseppe Pipoli

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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.

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BibTeX RIS

Barbara Nelli, Giuseppe Pipoli. 2021-10-08. Constant mean curvature hypersurfaces in $\mathbb H^n\times\mathbb R$ with small planar boundary. https://arxiv.org/abs/2110.03985

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