Indicators for Plurisubharmonic Functions of Logarithmic Growth
Complex Variables
2007-05-23 v1
Abstract
A notion of indicator for a plurisubharmonic function u of logarithmic growth in C^n is introduced and studied. It is applied to evaluation of the total Monge-Amp\`ere measure (dd^cu)^n({C}^n). Upper bounds for the measure are obtained in terms of growth characteristics of u. When u=log|f| for a polynomial mapping f with isolated zeros, the indicator generates the Newton polyhedron of f whose volume bounds the number of the zeros.
Keywords
Cite
@article{arxiv.math/9911240,
title = {Indicators for Plurisubharmonic Functions of Logarithmic Growth},
author = {Alexander Rashkovskii},
journal= {arXiv preprint arXiv:math/9911240},
year = {2007}
}
Comments
15 pages, LaTeX