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

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

2006-08-14

arxiv.org/abs/math/0608342v2

Geom. Dedicata 127 (2007), 1--5.

Mathematics

Differential Geometry

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

Scientific paper

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 $K_{N}\leq
-\kappa^{2}<0$. We show that ${\Hm}(N\times \mathbb{R})=\inf_{M\in {\mathscr
F}(N\times \mathbb{R})}\{| H_{M}| \}\geq (n-1)\kappa/n $.

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