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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 Γ in S2(3) with at least one smooth point, there exists an embedded H–plane PH in 3 with PH = Γ for any H [0,1).

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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