2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223213We 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.This is the version published by Geometry & Topology on 27 April 2006 (V3: typesetting corrections)Geometric TopologyDifferential Geometry53A10, 58B15text