p-convexity, p-plurisubharmonicity and the Levi problem
Differential Geometry
2017-12-12 v2 Analysis of PDEs
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 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.
Keywords
Cite
@article{arxiv.1111.3895,
title = {p-convexity, p-plurisubharmonicity and the Levi problem},
author = {F. Reese Harvey and H. Blaine Lawson},
journal= {arXiv preprint arXiv:1111.3895},
year = {2017}
}