IUMJ

Title: Symmetrization of plurisubharmonic and convex functions

Authors: Robert J Berman and Bo Berndtsson

Issue: Volume 63 (2014), Issue 2, 345-365

Abstract:

We show that Schwarz symmetrization does not increase the Monge-Ampere energy for $S^1$-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 other balanced domains except for complex ellipsoids, and discuss related questions for convex functions.