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Complex Analysis and Geometry pp 197–206Cite as

Themes on Non-analytic Singularities of Plurisubharmonic Functions

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 144))

Abstract

We survey some results and questions on the singularity of psh functions with non-analytic singularities. Also we show that the Demailly approximation sequence of a psh function does not contain a monotone singularity-increasing linear subsequence, in general.

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Acknowledgments

This work was supported by the National Research Foundation of Korea grants NRF-2012R1A1A1042764 and No.2011-0030795, funded by the Republic of Korea government.

The author would like to thank J.-P. Demailly for sharing many of his insights on the topic of this paper. He also thanks B. Berndtsson, Z. Błocki, S. Boucksom, V. Guedj, M. Păun and N. Sibony for valuable comments and discussions.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Seoul National University, 1 Gwanak-ro, Seoul, Gwanak-gu, 151-747, Korea

    Dano Kim

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  1. Dano Kim
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Correspondence to Dano Kim .

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Editors and Affiliations

  1. Department of Mathematics, Università di Roma Tor Vergata, Rome, Italy

    Filippo Bracci

  2. Dept. of Mathematics Education, Kyungnam University, Changwon, Korea (Republic of)

    Jisoo Byun

  3. Université Joseph Fourier Grenoble, Institut Fourier, Grenoble, France

    Hervé Gaussier

  4. Graduate School of Mathematical Sciences, The University of Tokyo, Meguro-ku, Tokyo, Japan

    Kengo Hirachi

  5. Department of Mathematics, POSTECH, Pohang, Korea (Republic of)

    Kang-Tae Kim

  6. Department of Mathematics, Bergische Universität Wuppertal, Wuppertal, Nordrhein-Westfalen, Germany

    Nikolay Shcherbina

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Kim, D. (2015). Themes on Non-analytic Singularities of Plurisubharmonic Functions. In: Bracci, F., Byun, J., Gaussier, H., Hirachi, K., Kim, KT., Shcherbina, N. (eds) Complex Analysis and Geometry. Springer Proceedings in Mathematics & Statistics, vol 144. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55744-9_14

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