On the Lelong-Demailly numbers of plurisubharmonic currents

TL;DR

This paper investigates the existence and estimates of Lelong-Demailly numbers for negative and positive plurisubharmonic currents in complex analysis, providing new insights into their behavior relative to specific functions.

Contribution

It establishes conditions for the existence of Lelong-Demailly numbers and derives estimates for these numbers for both positive and negative plurisubharmonic currents.

Findings

Existence conditions for Lelong-Demailly numbers of negative currents

Estimates for Lelong-Demailly numbers of positive currents

Estimates for Lelong-Demailly numbers of negative currents

Abstract

In this note we study the existence of the Lelong-Demailly number of a negative plurisubharmonic current with respect to a positive plurisubharmonic function on an open subset of $\C^n$. Then we establish some estimates of the Lelong-Demailly numbers of positive or negative plurisubharmonic currents.