IUMJ

Title: p-convexity, p-plurisubharmonicity, and the Levi problem

Authors: F. Reese Harvey and H. Blaine Lawson, Jr.

Issue: Volume 62 (2013), Issue 1, 149-169

Abstract:

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 union of the $p$-hull of the boundary with the "core" of the space. Lastly, the extreme rays in the convex cone of $p$-positive matrices are characterized. This is a basic result with many applications.