On cylindrically bounded $H$-Hypersurfaces of ${\mathbb{H}}^n\times \mathbb{R}$

Abstract

We show that $H$-hypersurfaces of ${\mathbb{H}}^n\times \mathbb{R}$ contained in a vertical cylinder and with Ricci curvature with strong quadratic decay have mean curvature $|H|>(n-1)/n$.

6 pages