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

Bessa, Gregorio Pacelli; Montenegro, J. Fabio

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

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Description

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 $.
We changed the title from a Remark on compact CMC-Hypersurfaces of $N\times \mathbb{R}$ to On compact and we added another theorem to the paper (theorem 1.4)