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

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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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