Uniqueness of Area Minimizing Surfaces for Extreme Curves
Differential Geometry
2015-03-20 v1 Geometric Topology
Abstract
Let M be a compact, orientable, mean convex 3-manifold with boundary. We show that the set of all simple closed curves in the boundary of M which bound unique area minimizing disks in M is dense in the space of simple closed curves in the boundary of M which are nullhomotopic in M. We also show that the set of all simple closed curves in the boundary of M which bound unique absolutely area minimizing surfaces in M is dense in the space of simple closed curves in the boundary of M which are nullhomologous in M.
Keywords
Cite
@article{arxiv.1207.4695,
title = {Uniqueness of Area Minimizing Surfaces for Extreme Curves},
author = {Baris Coskunuzer and Tolga Etgü},
journal= {arXiv preprint arXiv:1207.4695},
year = {2015}
}
Comments
14 pages, 3 figures