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On compact CMC-Hypersurfaces of $N\times \mathbb{R}$

Gregorio Pacelli Bessa·J. Fabio Montenegro
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Abstract

Let ${\mathscr F}(N\times \mathbb{R})$ be the set of all closed $H$-hypersurfaces $M\subset N\times \mathbb{R}$, where $N$ is a simply connected complete Riemannian $n$-manifold with sectional curvature $K_{N}\leq -κ^{2}<0$. We show that ${\Hm}(N\times \mathbb{R})=\inf_{M\in {\mathscr F}(N\times \mathbb{R})}\{| H_{M}| \}\geq (n-1)κ/n $.

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BibTeXRIS

Gregorio Pacelli Bessa, J. Fabio Montenegro. 2006-09-04. On compact CMC-Hypersurfaces of $N\times \mathbb{R}$. https://arxiv.org/abs/math/0608342

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