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

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

2003-12-30

arxiv.org/abs/math/0312508v3

Transactions of the Institute of Mathematics of the National Academy of Sciences of Ukraine, vol. 1, no. 1 (2004), pp. 169-191

Mathematics

Analysis of PDEs

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

Scientific paper

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.

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