Symmetrization of plurisubharmonic and convex functions Robert BermanBo Berndtsson 32U05PlurisubharmonicMonge-Ampere 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. Indiana University Mathematics Journal 2014 text pdf 10.1512/iumj.2014.63.5209 10.1512/iumj.2014.63.5209 en Indiana Univ. Math. J. 63 (2014) 345 - 365 state-of-the-art mathematics http://iumj.org/access/