Local property of maximal plurifinely plurisubharmonic functions

TL;DR

This paper establishes that continuous maximal plurifinely plurisubharmonic functions are characterized by their local maximality within the plurifine topology in complex analysis.

Contribution

It proves the equivalence between global and local maximality for continuous plurifinely plurisubharmonic functions, advancing understanding in pluripotential theory.

Findings

Continuous $$-plurisubharmonic functions are $$-maximal iff locally $$-maximal

Provides a local-global characterization in plurifine topology

Enhances theoretical framework of pluripotential theory

Abstract

In this paper, we prove that a continuous $\mathcal F$-plurisubharmonic functions defined in an $\mathcal F$-open set in $\mathbb C^n$ is $\mathcal F$-maximal if and only if it is $\mathcal F$-locally $\mathcal F$-maximal.