Existence of proper minimal surfaces of arbitrary topological type

Ferrer, Leonor; Martin, Francisco; Meeks III, William H.

Existence of proper minimal surfaces of arbitrary topological type

Authors

Ferrer, Leonor

Martin, Francisco

Meeks III, William H.

Description

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.
33 pages, 10 figures