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October 2020 The Lelong number, the Monge–Ampère mass, and the Schwarz symmetrization of plurisubharmonic functions
Long Li
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Ark. Mat. 58(2): 369-392 (October 2020). DOI: 10.4310/ARKIV.2020.v58.n2.a8

Abstract

The aim of this paper is to study the Lelong number, the integrability index and the Monge–Ampère 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–Ampère mass is always decreasing under the symmetrization.

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Long Li. "The Lelong number, the Monge–Ampère mass, and the Schwarz symmetrization of plurisubharmonic functions." Ark. Mat. 58 (2) 369 - 392, October 2020. https://doi.org/10.4310/ARKIV.2020.v58.n2.a8

Information

Received: 25 May 2019; Revised: 2 September 2019; Published: October 2020
First available in Project Euclid: 16 January 2021

Digital Object Identifier: 10.4310/ARKIV.2020.v58.n2.a8

Rights: Copyright © 2020 Institut Mittag-Leffler

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Vol.58 • No. 2 • October 2020
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