Partial pluricomplex energy and integrability exponents of plurisubharmonic functions

TL;DR

This paper establishes a sufficient condition based on Monge-Ampère mass for the local integrability of exponential functions of plurisubharmonic functions, providing a pluripotential theoretic proof of Demailly's theorem.

Contribution

It introduces a new sufficient condition linking Monge-Ampère mass to integrability, offering a novel proof of a key theorem in pluripotential theory.

Findings

A specific Monge-Ampère mass condition ensures local integrability.

Provides a new pluripotential theoretic proof of Demailly's theorem.

Enhances understanding of integrability exponents of plurisubharmonic functions.

Abstract

We give a sufficient condition on the Monge-Amp\`ere mass of a plurisubharmonic function $u$ for $\exp (- 2 u)$ to be locally integrable. This gives a pluripotential theoretic proof of a theorem by J-P. Demailly.