Properly Embedded Least Area Planes in Gromov Hyperbolic 3-Spaces
Geometric Topology
2011-11-09 v2 Differential Geometry
Abstract
We show that for any simple closed curve in the sphere at infinity of a Gromov hyperbolic 3-space with cocompact metric, there exist a properly embedded least area plane in the space spanning the given curve. This gives a positive answer to a conjecture of Gabai. Soma has already proven this conjecture earlier. Our technique here is simpler and more general, and it can be applied to many similar settings.
Cite
@article{arxiv.math/0609099,
title = {Properly Embedded Least Area Planes in Gromov Hyperbolic 3-Spaces},
author = {Baris Coskunuzer},
journal= {arXiv preprint arXiv:math/0609099},
year = {2011}
}