Maximal Plurifinely Plurisubharmonic functions
Complex Variables
2014-06-23 v2
Abstract
The main purpose of this paper is to introduce and study the notion of plurifinely-maximal plurifinely plurisubharmonic functions, which extends the notion of maximal plurisubharmonic functions on a Euclidean domain to a plurifine domain of C^n in a natural way. Our main result is that a finite plurifinely plurisubharmonic function u on a plurifine domain U satisfies (dd^c u)^n=0 if and only if u is plurifinely-locally plurifinely-maximal outside some pluripolar set. In particular, a finite plurifinely-maximal plurisubharmonic function u satisfies (dd^c u)^n=0.
Cite
@article{arxiv.1311.0513,
title = {Maximal Plurifinely Plurisubharmonic functions},
author = {Mohamed El Kadiri and Iris Marjan Smit},
journal= {arXiv preprint arXiv:1311.0513},
year = {2014}
}
Comments
20 pages, manuscript as accepted by publisher. To appear in Potential Analysis