Symmetrization of plurisubharmonic and convex functions

Details Symmetrization of plurisubharmonic and convex functions Symmetrization of plurisubharmonic and convex functions

2012-04-04

arxiv.org/abs/1204.0931v1

Mathematics

Complex Variables

16 pages

Scientific paper

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 and discuss related
questions for convex functions.

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