Additivity of the approximation functional of currents induced by Bergman kernels

TL;DR

This paper proves that the approximation functional of certain positive currents, induced by Bergman kernels, is additive, confirming a question posed by Demailly in 2013.

Contribution

It establishes the additivity property of the approximation functional for currents induced by Bergman kernels, answering a longstanding open question.

Findings

Proves additivity of the approximation functional

Confirms a conjecture by Demailly from 2013

Advances understanding of currents and Bergman kernel interactions

Abstract

In this note, we give a positive answer to a question raised by Jean-Pierre Demailly in 2013, and show the additivity of the approximation functional of closed positive $(1,1)$-currents induced by Bergman kernels.