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
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10.1512/iumj.2014.63.5209
10.1512/iumj.2014.63.5209
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Indiana Univ. Math. J. 63 (2014) 345 - 365
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