Subharmonic functions, mean value inequality, boundary behavior, nonintegrability and exceptional sets

TL;DR

This paper explores advanced properties of subharmonic functions, including mean value inequalities, boundary behavior, nonintegrability, and improvements to singularity removal results, contributing to the theoretical understanding of these functions.

Contribution

It provides partial improvements to Blanchet's removable singularity results for subharmonic, plurisubharmonic, and convex functions, and discusses boundary behavior and nonintegrability.

Findings

Enhanced boundary behavior results for subharmonic functions

Borderline case analysis of nonintegrability for superharmonic functions

Improved criteria for removable singularities in subharmonic and related functions

Abstract

We begin by shortly recalling a generalized mean value inequality for subharmonic functions, and two applications of it: first a weighted boundary behavior result (with some new references and remarks), and then a borderline case result to Suzuki's nonintegrability results for superharmonic and subharmonic functions. The main part of the talk consists, however, of partial improvements to Blanchet's removable singularity results for subharmonic, plurisubharmonic and convex functions.