#### Volume 20, issue 1 (2016)

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Asymptotic $H$–Plateau problem in $\mathbb{H}^3$

### Baris Coskunuzer

Geometry & Topology 20 (2016) 613–627
##### Abstract

We show that for any Jordan curve $\Gamma$ in ${S}_{\infty }^{2}\left({ℍ}^{3}\right)$ with at least one smooth point, there exists an embedded $H\phantom{\rule{0.3em}{0ex}}$–plane ${\mathsc{P}}_{H}$ in ${ℍ}^{3}$ with ${\partial }_{\infty }{\mathsc{P}}_{H}=\Gamma$ for any $H\in \left[0,1\right)$.

##### Keywords
asymptotic Plateau problem, constant mean curvature, $H$–surfaces, hyperbolic space
Primary: 53A10