Asymptotic H–Plateau problem in ℍ3

Coskunuzer, Baris

doi:10.2140/gt.2016.20.613

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

Baris Coskunuzer

Geometry & Topology 20 (2016) 613–627

DOI: 10.2140/gt.2016.20.613

Abstract

We show that for any Jordan curve $Γ$ in $S_{\infty}^{2} (ℍ^{3})$ with at least one smooth point, there exists an embedded $H$ –plane $P_{H}$ in $ℍ^{3}$ with $\partial_{\infty} P_{H} = Γ$ for any $H \in [0, 1)$ .

Keywords

asymptotic Plateau problem, constant mean curvature, $H$–surfaces, hyperbolic space

Mathematical Subject Classification 2010

Primary: 53A10

References

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

Volume 20, issue 1 (2016)