Symmetrization of plurisubharmonic and convex functions
  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 general balanced domains except for complex ellipsoids and discuss related questions for convex functions. 
Robert J. Berman and Bo Berndtsson
math.CV math.FA