2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224542Consider 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 figuresDifferential Geometry53A10; 49Q05text