Local Indicators for Plurisubharmonic Functions
Complex Variables
2007-05-23 v1
Abstract
A notion of local indicator for a plurisubharmonic function is introduced. The indicator is a certain plurisubharmonic function in the unit polydisc, which controls the behavior of the considered function near a fixed point of its singularity, as well as the residual Monge-Ampere mass of the function at this point. A pluricomplex Green function with respect to given indicators is constructed and applied to the Dirichlet problem for the Monge- Ampere operator in the class of plurisubharmonic functions with isolated singularities.
Cite
@article{arxiv.math/9901014,
title = {Local Indicators for Plurisubharmonic Functions},
author = {Pierre Lelong and Alexander Rashkovskii},
journal= {arXiv preprint arXiv:math/9901014},
year = {2007}
}
Comments
18 pages, LaTeX; to appear in J. Math. Pures Appl