On the directional Lelong–Demailly numbers of positive currents

Abstract

In this paper, we study the existence of the directional Lelong–Demailly numbers of positive plurisubharmonic or plurisuperharmonic currents. We prove the independence of these numbers of the system of coordinates. Moreover, these numbers will be given by locally integrable functions.

Keywords:

• Lelong number
• positive plurisubharmonic current
• plurisubharmonic function

AMS Subject Classifications:

• 32U25
• 32U40
• 32U05