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Indicators for Plurisubharmonic Functions of Logarithmic Growth

Alexander Rashkovskii
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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-Ampère 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.

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Alexander Rashkovskii. 1999-11-30. Indicators for Plurisubharmonic Functions of Logarithmic Growth. https://arxiv.org/abs/math/9911240

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