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arXiv · 1905.10652

The Lelong number, the Monge-Amp\`ere mass and the Schwarz symmetrization of plurisubharmonic functions

Long Li
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Abstract

The aim of this paper is to study the Lelong number, the integrability index and the Monge-Amp\`ere mass at the origin of an $S^1$-invariant plurisubharmonic function on a balanced domain in $\mathbb{C}^n$ under the Schwarz symmetrization. We prove that $n$ times the integrability index is exactly the Lelong number of the symmetrization, and if the function is further toric with a single pole at the origin, then the Monge-Amp\`ere mass is always decreasing under the symmetrization

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Long Li. 2019-05-25. The Lelong number, the Monge-Amp\`ere mass and the Schwarz symmetrization of plurisubharmonic functions. https://arxiv.org/abs/1905.10652

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