English

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.

Keywords

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