Slab Theorem and Halfspace Theorem for constant mean curvature surfaces in ${\mathbb{H}}^2\times \mathbb{R}$

Laurent Hauswirth, Ana Menezes, Magdalena Rodriguez

We prove that a properly embedded annular end of a surface in ${\mathbb{H}}^2\times \mathbb{R}$ with constant mean curvature $0<H\le \frac{1}{2}$ can not be contained in any horizontal…