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

Long Li Science Institute, University of Iceland, Reykjavik, Iceland

TBD mathscidoc:2203.43015

Arkiv for Matematik, 58, (2), 369-392, 2020.11
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 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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@inproceedings{long2020the,
  title={The Lelong number, the Monge–Ampère mass, and the Schwarz symmetrization of plurisubharmonic functions},
  author={Long Li},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220311101657201216948},
  booktitle={Arkiv for Matematik},
  volume={58},
  number={2},
  pages={369-392},
  year={2020},
}
Long Li. The Lelong number, the Monge–Ampère mass, and the Schwarz symmetrization of plurisubharmonic functions. 2020. Vol. 58. In Arkiv for Matematik. pp.369-392. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220311101657201216948.
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