46 research outputs found
Generic uniqueness of least area planes in hyperbolic space
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.Comment: This is the version published by Geometry & Topology on 27 April 2006
(V3: typesetting corrections
Number of Least Area Planes in Gromov Hyperbolic 3-Spaces
We show that for a generic simple closed curve C in the asymptotic boundary
of a Gromov hyperbolic 3-space with cocompact metric X, there exist a unique
least area plane P in X with asymptotic boundary C. This result has interesting
topological applications for constructions of canonical 2-dimensional objects
in 3-manifolds