Minimal surfaces in a cone

We prove the convex hull property for properly immersed minimal hypersurfaces in a cone of bb R-n. We deal with the existence of new barriers for the maximum principle application in noncompact truncated tetrahedral domains of bb R-3, describing the space of such domains admitting barriers of this kind. Nonexistence results for nonflat minimal surfaces whose boundary lies in opposite faces of a tetrahedral domain are obtained. Finally, new simple closed subsets of bb R-3 which have the property of intersecting any properly immersed minimal surface are shown.