Lelong数，monge - ampantere质量，和多重次谐波函数的Schwarz对称

IF 0.8 4区数学 Q2 MATHEMATICS Arkiv for Matematik Pub Date : 2019-05-25 DOI:10.4310/arkiv.2020.v58.n2.a8

Long Li

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引用次数: 2

摘要

在Schwarz对称下，研究了$\mathbb{C}^n$中平衡域上$S^1$不变多次谐波函数的Lelong数、可积性指标和原点处的Monge-Ampere质量。我们证明了$n$乘以可积性指标正是对称化的Lelong数，并且如果函数在原点处为单极进一步环面，则在对称化下蒙日-安培质量总是减小的

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The Lelong number, the Monge–Ampère mass, and the Schwarz symmetrization of plurisubharmonic functions

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

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