1999/11/30 by Alexander Rashkovskii, Rashkovskii, Alexander · 1 citation
Computer Science · Mathematics · #32F05 #32F07 #Advanced Mathematical Modeling in Engineering #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV #msc:32F05 #msc:32F07
paper · pdf · doi:10.48550/arxiv.math/9911240
15 pages, LaTeX
arxiv created 1999/11/30 · openalex publication_date 1999/11/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A notion of indicator for a plurisubharmonic function u of logarithmic growth in Cn is introduced and studied. It is applied to evaluation of the total Monge-Ampère measure (ddcu)n(Cn). 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.