p-convexity, p-plurisubharmonicity and the Levi problem

F. Reese Harvey; H. Blaine Lawson Jr

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arXiv · 1111.3895

p-convexity, p-plurisubharmonicity and the Levi problem

F. Reese Harvey·H. Blaine Lawson Jr

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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.

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F. Reese Harvey, H. Blaine Lawson Jr. 2011-11-16. p-convexity, p-plurisubharmonicity and the Levi problem. https://arxiv.org/abs/1111.3895

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