Pluri-polarity in almost complex structures

TL;DR

This paper investigates the pluripolarity of $J$-holomorphic curves in almost complex structures, highlighting their limitations in being represented as minus-infinity sets of certain plurisubharmonic functions.

Contribution

It clarifies the pluripolar nature of $J$-holomorphic curves and their inability to be characterized by specific logarithmic singularities.

Findings

$J$-holomorphic curves are pluripolar.

They cannot be minus-infinity sets of plurisubharmonic functions with logarithmic singularity.

Abstract

$J$-holomorphic curves are pluripolar, but they are not minus-infinity sets of pluri-subharmonic functions with logarithmic singularity.