A new plurisubharmonic capacity and functions holomorphic along holomorphic vector fields

2022/11/10 by Ye-Won Luke Cho, Cho, Ye-Won Luke
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2211.05615

openalex publication_date 2022/11/10 · openalex created_date 2022/11/16 · openalex updated_date 2026/07/28

Abstract

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 \citeSiciak82. Our main theorem improves the results of \citeKPS09, \citeCho22 as well as the original Forelli's theorem.

Related

• Continuous analytic capacity and holomorphic motions
• Localization of Forelli's theorem
• Continuity of capacity of a holomorphic motion
• On the generalization of Forelli's theorem
• Siciak's homogeneous extremal functions, holomorphic extension and a generalization of Helgason's support theorem