p-convexity, p-plurisubharmonicity and the Levi problem
  Three results in p-convex geometry are established. First is the analogue of the Levi problem in several complex variables, namely: local p-convexity implies global p-convexity. The second asserts that the support of a minimal p-dimensional current is contained in the p-hull of the boundary union with the "core" of the space. Lastly, the exteme rays in the convex cone of p-positive matrices are characterized. This is a basic result with many applications. 
F. Reese Harvey and H. Blaine Lawson Jr
math.DG math.AP