On a problem of CHirka

TL;DR

This paper demonstrates that plurisubharmonic functions can be extended across certain singularities using a modified method, solving a problem posed by Chirka.

Contribution

It introduces a slight adjustment to existing methods, enabling extension of plurisubharmonic functions across measure-zero singularities, addressing Chirka's problem.

Findings

Plurisubharmonic functions extend across measure-zero singularities.

A modified method of Caffarelli, Li, and Nirenberg is effective.

The result solves a previously open problem by Chirka.

Abstract

We observe that a slight adjustment of a method of Caffarelli, Li, and Nirenberg yields that plurisubharmonic functions extend across subharmonic singularities as long as the singularities form a closed set of measure zero. This solves a problem posed by Chirka.