A half-space theorem for graphs of constant mean curvature $0<H<\frac{1}{2}$ in $\mathbb{H}^{2}\times\mathbb{R}$

Abstract

We study a half-space problem related to graphs in $\mathbb{H}^{2}\times\mathbb{R}$, where $\mathbb{H}^{2}$ is the hyperbolic plane, having constant mean curvature $H$ defined over unbounded domains in $\mathbb{H}^{2}$.