Generic uniqueness of least area planes in hyperbolic space

Coskunuzer, Baris

doi:10.2140/gt.2006.10.401

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Generic uniqueness of least area planes in hyperbolic space

Baris Coskunuzer

Geometry & Topology 10 (2006) 401–412

DOI: 10.2140/gt.2006.10.401

arXiv: math.GT/0408066

Abstract

We study the number of solutions of the asymptotic Plateau problem in $ℍ^{3}$ . By using the analytical results in our previous paper, and some topological arguments, we show that there exists an open dense subset of $C^{3}$ Jordan curves in $S_{\infty}^{2} (ℍ^{3})$ such that any curve in this set bounds a unique least area plane in $ℍ^{3}$ .

Keywords

least area plane, asymptotic Plateau problem

Mathematical Subject Classification 2000

Primary: 53A10

Secondary: 58B15

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Publication

Received: 5 August 2004

Accepted: 27 March 2006

Published: 27 April 2006

Proposed: Gang Tian

Seconded: Tobias Colding, David Gabai

Authors

Baris Coskunuzer
Department of Mathematics Yale University New Haven CT 06520 USA

Volume 10, issue 1 (2006)