  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.
