Constant mean curvature graphs in ${\mathbb{H}}^3$ defined in exterior domains

Patricia Klaser, Adilson Nunes, Jaime Ripoll

Given $H\in [0,1)$ and given a $C^0$ exterior domain $\Omega$ in a $H-$hypersphere of ${\mathbb{H}}^3,$ the existence of hyperbolic Killing graphs of CMC $H$ defined in $\overline{\Omega }$ with…