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Estimates of Level Sets of Holomorphic Functions and Applications to the Weighted Log Canonical Thresholds

The Journal of Geometric Analysis volume 31, pages 3783–3819 (2021)Cite this article

Abstract

In this paper, we establish some estimates of level sets of holomorphic functions. Relying on obtained estimates we compute some of the weighted log canonical thresholds of plurisubharmonic functions. Finally, we prove the analyticity of the sublevel sets of weighted log canonical thresholds of plurisubharmonic functions.

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Acknowledgements

The authors are grateful to the referees for carefully reading , valuable comments and suggestions that led to improvements of the exposition of the paper. The second-named author was funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.02-2017.306.

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Authors and Affiliations

  1. Department of Mathematics, Hanoi National University of Education, Hanoi, Vietnam

    Le Mau Hai & Trinh Tung

  2. International Centre for Research and Postgraduate Training in Mathematics, Institute of Mathematics Vietnam Academy of Science and Technology, 18-Hoang Quoc Viet, Hanoi, Vietnam

    Pham Hoang Hiep

Authors
  1. Le Mau Hai
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  2. Pham Hoang Hiep
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  3. Trinh Tung
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Correspondence to Le Mau Hai.

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Hai, L.M., Hiep, P.H. & Tung, T. Estimates of Level Sets of Holomorphic Functions and Applications to the Weighted Log Canonical Thresholds. J Geom Anal 31, 3783–3819 (2021). https://doi.org/10.1007/s12220-020-00414-1

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  • DOI: https://doi.org/10.1007/s12220-020-00414-1

Keywords

  • Estimates of level sets of holomorphic functions
  • Weighted log canonical thresholds
  • Plurisubharmonic functions
  • Weierstrass polynomials

Mathematics Subject Classification

  • 14B05
  • 32S05
  • 32U25
  • 32W20