Existence of proper minimal surfaces of arbitrary topological type
Differential Geometry
2009-03-26 v1
Abstract
Consider a domain D in R^3 which is convex (possibly all R^3) or which is smooth and bounded. Given any open surface M, we prove that there exists a complete, proper minimal immersion f : M --> D. Moreover, if D is smooth and bounded, then we prove that the immersion f : M --> D can be chosen so that the limit sets of distinct ends of M are disjoint connected compact sets in the boundary of D.
Cite
@article{arxiv.0903.4194,
title = {Existence of proper minimal surfaces of arbitrary topological type},
author = {Leonor Ferrer and Francisco Martin and William H. Meeks},
journal= {arXiv preprint arXiv:0903.4194},
year = {2009}
}
Comments
33 pages, 10 figures