p-convexity, p-plurisubharmonicity and the Levi problem

By F. R. Harvey, H. Lawson, jr.. 2011

105 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1f574bae212b76b0112f3b89d51518c94fa6d2dc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Julio D. Rossi
2. Pablo Blanc
3. Jorge García-Melián
4. Mayte Pérez-Llanos
5. Wenxian Shen

In Geometry and Topology

1. Julio D. Rossi
2. Pablo Blanc

Citations in the corpus

• Games for eigenvalues of the Hessian and concave/convex envelopes (2018, methodology): “In particular, we can handle equations of the form or a convex combination of the previous two These operators appear in [2, 3, 6, 7] and in [13, 14] with connections with geometry.”