Existence of proper minimal surfaces of arbitrary topological type

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.

33 pages, 10 figures

References in corpus (1)

• Density theorems for complete minimal surfaces in R^3

Cited by in corpus (4)

• Doubling and Desingularization Constructions for Minimal Surfaces
• Null Curves in ${\mathbb{C}}^3$ and Calabi-Yau Conjectures
• Calabi-Yau domains in three manifolds
• Complete minimal surfaces and harmonic functions