A New Plurisubharmonic Capacity and Functions Holomorphic Along Holomorphic Vector Fields

The main purpose of this article is to present a generalization of Forelli’s theorem for functions holomorphic along a suspension of integral curves of a diagonalizable vector field of aligned type. For this purpose, we develop a new capacity theory that generalizes the theory of projective capacity...

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Bibliographic Details
Published inThe Journal of geometric analysis Vol. 33; no. 8
Main Author Cho, Ye-Won Luke
Format Journal Article
LanguageEnglish
Published New York Springer US 01.08.2023
Springer Nature B.V
Subjects
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fields (mathematics)
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Harmonic functions
Mathematical analysis
Mathematics
Mathematics and Statistics
Theorems
32A05
Foliation of vector fields
32U20
Complex-analyticity
32S65
32A10
32M25
Pluripotential theory
Forelli’s theorem
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Summary:The main purpose of this article is to present a generalization of Forelli’s theorem for functions holomorphic along a suspension of integral curves of a diagonalizable vector field of aligned type. For this purpose, we develop a new capacity theory that generalizes the theory of projective capacity introduced by Siciak (Sophia Kokyuroku Math 14:1–96, 1982). Our main theorem improves the results of Kim et al. (J Geom Anal 19(3):655–666, 2009) and Cho (Complex Var. Elliptic Equ., 2022) as well as the original Forelli’s theorem.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-023-01321-x