Generic uniqueness of least area planes in hyperbolic space

Details Generic uniqueness of least area planes in hyperbolic space Generic uniqueness of least area planes in hyperbolic space

2004-08-04

arxiv.org/abs/math/0408066v3

Geom. Topol. 10 (2006) 401-412

Mathematics

Geometric Topology

This is the version published by Geometry & Topology on 27 April 2006 (V3: typesetting corrections)

Scientific paper

10.2140/gt.2006.10.401

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^2_{infty}(H^3) such that any curve in this set bounds a unique least area
plane in H^3.

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