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arXiv · 1204.0931

Symmetrization of plurisubharmonic and convex functions

Robert J. Berman·Bo Berndtsson
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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 general balanced domains except for complex ellipsoids and discuss related questions for convex functions.

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Robert J. Berman, Bo Berndtsson. 2012-04-04. Symmetrization of plurisubharmonic and convex functions. https://arxiv.org/abs/1204.0931

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