2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71337Consider a convex domain B of space. We prove that there exist complete minimal surfaces which are properly immersed in B. We also demonstrate that if D and D' are convex domains with D bounded and the closure of D contained in D' then any minimal disk whose boundary lies in the boundary of D, can be approximated in any compact subdomain of D by a complete minimal disk which is proper in D'. We apply these results to study the so called type problem for a minimal surface: we demonstrate that the interior of any convex region is not a universal region for minimal surfaces, in the sense explained by Meeks and Perez.26 pages, 7 figuresGeneral MathematicsDifferential GeometryPrimary 53A10; Secondary 49Q05, 49Q10, 53C42text