Mathematics – Differential Geometry
Scientific paper
2008-04-08
Mathematics
Differential Geometry
Scientific paper
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.
Harvey Reese F.
Lawson Blaine H. Jr.
No associations
LandOfFree
Plurisubharmonicity in a General Geometric Context does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Plurisubharmonicity in a General Geometric Context, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Plurisubharmonicity in a General Geometric Context will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-540857