Number of Least Area Planes in Gromov Hyperbolic 3-Spaces
Geometric Topology
2010-05-03 v1 Differential Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.0805.1978,
title = {Number of Least Area Planes in Gromov Hyperbolic 3-Spaces},
author = {Baris Coskunuzer},
journal= {arXiv preprint arXiv:0805.1978},
year = {2010}
}