Volume 10, issue 1 (2006)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Generic uniqueness of least area planes in hyperbolic space

Baris Coskunuzer

Geometry & Topology 10 (2006) 401–412

arXiv: math.GT/0408066

Abstract

We study the number of solutions of the asymptotic Plateau problem in 3. By using the analytical results in our previous paper, and some topological arguments, we show that there exists an open dense subset of C3 Jordan curves in S2(3) such that any curve in this set bounds a unique least area plane in 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