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

Abstract

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 boundary $\partial \Omega$ included in the $H-$hypersphere is obtained.

References in corpus (1)

• Constant mean curvature surfaces in ${\mathbb{H}}^2\times \mathbb{R}$ with boundary in two parallel planes