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

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.

13 pages; a talk at the International Workshop on Potential Theory and Free Boundary Flows, Ukraine, Kiev, 19-27 August 2003

Cited by in corpus (2)

• On an inequality related to the radial growth of quasinearly subharmonic functions in locally uniformly homogeneous spaces
• Removability results for subharmonic functions, for separately subharmonic functions, for harmonic functions, for separately harmonic functions and for holomorphic functions, a survey