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Equidistribution of non-pluripolar products associated with quasi-plurisubharmonic functions of finite energy

Authors: Taeyong Ahn and Ngoc Cuong Nguyen
Journal: Proc. Amer. Math. Soc. 148 (2020), 719-729
MSC (2010): Primary 32U40, 37F10
Published electronically: August 7, 2019
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Abstract: In this article, we consider currents given by the $ p$-fold non-pluripolar product associated with a quasi-plurisubharmonic function of finite energy, and prove that normalized pull-backs of such currents converge to the Green $ (p, p)$-current exponentially fast in the sense of currents for holomorphic endomorphisms of $ \mathbb{P}^k$.

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Taeyong Ahn
Affiliation: Department of Mathematics Education, Inha University, 100 Inha-ro, Michuhol-gu, Incheon 22212, Republic of Korea

Ngoc Cuong Nguyen
Affiliation: Faculty of Mathematics and Computer Science, Jagiellonian University 30-348 Kraków, Łojasiewicza 6, Poland

Keywords: Pluripotential theory, non-pluripolar product, Cegrell class, equidistribution, Green current
Received by editor(s): November 19, 2018
Received by editor(s) in revised form: January 2, 2019, May 29, 2019, and June 1, 2019
Published electronically: August 7, 2019
Additional Notes: The first author was supported by INHA UNIVERSITY Research Grant (INHA-57850)
A part of the work was done while the second author was a postdoc at Postech University, which was financially supported by the NRF Grant 2011-0030044 (SRC-GAIA) of The Republic of Korea. The second author was also partially supported by NCN grant 2017/27/B/ST1/01145
Communicated by: Filippo Bracci
Article copyright: © Copyright 2019 American Mathematical Society