Symmetrization of plurisubharmonic and convex functions
Complex Variables
2012-10-30 v2 Functional Analysis
Abstract
We show that Schwarz symmetrization does not increase the Monge-Ampere energy for -invariant plurisubharmonic functions in the ball. As a result we derive a sharp Moser-Trudinger inequality for such functions. We also show that similar results do not hold for general balanced domains except for complex ellipsoids and discuss related questions for convex functions.
Keywords
Cite
@article{arxiv.1204.0931,
title = {Symmetrization of plurisubharmonic and convex functions},
author = {Robert J. Berman and Bo Berndtsson},
journal= {arXiv preprint arXiv:1204.0931},
year = {2012}
}
Comments
16 pages. In the revised version a problem that was left open in the original version has been solved