English

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}
}