Plurisubharmonicity in a General Geometric Context

By F. R. Harvey, H. Lawson. 2008

56 citations recorded by the source corpus.

Recently the authors have explored new concepts of plurisubharmonicity and pseudoconvexity, with much of the attendant analysis, in the context of calibrated manifolds. Here a much broader extension is made. This development covers a wide variety of geometric situations, including, for example, Lagrangian plurisubhamonicity and convexity. It also applies in a number of non-geometric situations. Results include: fundamental properties of $P^+$-plurisubharmonic functions, plurisubharmonic distributions and regularity, $P^+$-convex domains and $P^+$-convex boundaries, topological restrictions on and construction of such domains, continuity of upper envelopes, and solutions of the Dirichlet problem for related Monge-Ampere-type equations. Many results in this paper have been generalized in recent work of the authors. However, this article covers many cases of geometric interest, and certain convexity assumptions here allow the use of classical analytic methods, making the exposition more accessible.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4197700207f4b6eb2ff7f46a26b4e3d7688bf7c3

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

An introduction to potential theory in calibrated geometry (2007, background): “See [ HL4 ] for a more comprehensive development, which is also calibration independent.”