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arxiv: math/9911240 · v1 · submitted 1999-11-30 · 🧮 math.CV

Indicators for Plurisubharmonic Functions of Logarithmic Growth

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keywords growthboundsindicatorlogarithmicmeasureplurisubharmoniczerosapplied
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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.

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