Constant mean curvature hypersurfaces in ${\mathbb{H}}^n\times \mathbb{R}$ with small planar boundary

Barbara Nelli, Giuseppe Pipoli

We show that constant mean curvature hypersurfaces in ${\mathbb{H}}^n\times \mathbb{R}$, with small and pinched boundary contained in a horizontal slice $P$ are topological disks, provi…