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
Publication
Received: 20 March 2015
Revised: 7 May 2015
Accepted: 7 June 2015
Published: 29 February 2016
Proposed: Tobias H Colding
Seconded: Dmitri Burago, Gang Tian
Authors
 Baris Coskunuzer Massachusetts Institute of Technology Mathematics Department Cambridge, MA 02139 USA Department of Mathematics Koç University Istanbul 34450 Turkey