Complete pluripolar sets and removable singularities of plurisubharmonic functions

TL;DR

This paper proves a Hartogs type extension theorem for plurisubharmonic functions across compact complete pluripolar sets, expanding understanding of removable singularities in complex analysis.

Contribution

It introduces a new extension theorem for plurisubharmonic functions across complete pluripolar sets, complementing classical results.

Findings

Extension theorem for plurisubharmonic functions across pluripolar sets

Characterization of removable singularities in complex analysis

Advancement in understanding pluripolar set properties

Abstract

Inspired by Chen-Wu-Wang (Math. Ann. 362: 305--319, 2015), we prove a Hartogs type extension theorem for plurisubharmonic functions across a compact complete pluripolar set, which is complementary to a classical theorem of Shiffman.