English

A new plurisubharmonic capacity and functions holomorphic along holomorphic vector fields

Complex Variables 2023-05-23 v3

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 \cite{Siciak82}. Our main theorem improves the results of \cite{KPS09}, \cite{Cho22} as well as the original Forelli's theorem.

Keywords

Cite

@article{arxiv.2211.05615,
  title  = {A new plurisubharmonic capacity and functions holomorphic along holomorphic vector fields},
  author = {Ye-Won Luke Cho},
  journal= {arXiv preprint arXiv:2211.05615},
  year   = {2023}
}

Comments

30 pages. Comments are welcome. The final version is to appear in The Journal of Geometric Analysis

R2 v1 2026-06-28T05:36:17.074Z