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

Gregorio Pacelli Bessa; J. Fabio Montenegro

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

Differential Geometry 2008-05-06 v2

Authors: Gregorio Pacelli Bessa , J. Fabio Montenegro

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

Keywords

cmc hypersurfaces riemannian manifolds sectional curvature compact hypersurfaces n×r product

Cite

@article{arxiv.math/0608342,
  title  = {On compact CMC-Hypersurfaces of $N\times \mathbb{R}$},
  author = {Gregorio Pacelli Bessa and J. Fabio Montenegro},
  journal= {arXiv preprint arXiv:math/0608342},
  year   = {2008}
}

Comments

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)

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

Abstract

Keywords

Cite

Comments

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