Embedded Plateau Problem
Differential Geometry
2011-12-13 v2 Geometric Topology
Abstract
We show that if C is a simple closed curve bounding an embedded disk in a closed 3-manifold M, then there exists a disk D in M with boundary C such that D minimizes the area among the embedded disks with boundary C. Moreover, D is smooth, minimal and embedded everywhere except where the boundary C meets the interior of D. The same result is also valid for homogenously regular manifolds with sufficiently convex boundary.
Cite
@article{arxiv.1005.1723,
title = {Embedded Plateau Problem},
author = {Baris Coskunuzer},
journal= {arXiv preprint arXiv:1005.1723},
year = {2011}
}