Analyticity and propagation of plurisubharmonic singularities

TL;DR

This paper extends Siu's analyticity theorem to relative types of plurisubharmonic functions, explores how singularities propagate, and examines the maximality of pluricomplex Green functions with analytic singularities.

Contribution

It introduces a variant of Siu's theorem for relative types and investigates singularity propagation and Green function maximality in complex analysis.

Findings

Proved a variant of Siu's analyticity theorem for relative types.

Derived results on the propagation of plurisubharmonic singularities.

Analyzed the maximality of pluricomplex Green functions with analytic singularities.

Abstract

A variant of Siu's analyticity theorem is proved for relative types of plurisubharmonic functions. Some results on propagation of plurisubharmonic singularities and maximality of pluricomplex Green functions with analytic singularities are derived.