Removability results for subharmonic functions, for separately subharmonic functions, for harmonic functions, for separately harmonic functions and for holomorphic functions, a survey

TL;DR

This survey reviews recent and classical results on the removability and extension of various classes of functions, including subharmonic, harmonic, separately harmonic, and holomorphic functions, highlighting improvements and connections to established theorems.

Contribution

The paper provides new extension results for these functions, improving previous theorems and relating them to classical results by Besicovitch and Shiffman.

Findings

Improved extension theorem for subharmonic functions.

Extension results for separately subharmonic, harmonic, and separately harmonic functions.

Connections established between holomorphic function extensions and classical theorems.

Abstract

We begin with an improvement to an extension result for subharmonic functions of Blanchet et al. With the aid of this improvement we then give extension results for subharmonic functions, for separately subharmonic functions, for harmonic functions, for separately harmonic functions and for holomorphic functions. Our results for holomorphic functions are related to Besicovitch's and Shiffman's well-known extension results, at least in some sense. Moreover, we recall another, slightly related and previous extension result for holomorphic functions.