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

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

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 plur...

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Veröffentlicht in:The Journal of Geometric Analysis 2021-04, Vol.31 (4), p.3783-3819
Hauptverfasser: Hai, Le Mau, Hiep, Pham Hoang, Tung, Trinh
Format: Artikel
Sprache:eng
Schlagworte:
Abstract Harmonic Analysis
Analytic functions
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Estimates
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Harmonic functions
Mathematical analysis
Mathematics
Mathematics and Statistics
Thresholds
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Zusammenfassung: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.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-020-00414-1