A generalization of Poletsky's classical theorem and a characterization of thinness of a subset in $\C^n$

TL;DR

This paper extends Poletsky's classical theorem to cases with non-upper semicontinuous kernels and characterizes the thinness of subsets in complex space using analytic discs.

Contribution

It generalizes Poletsky's theorem to broader conditions and provides a new analytic disc-based characterization of thinness in complex analysis.

Findings

Generalization of Poletsky's theorem to non-upper semicontinuous kernels

Characterization of thinness via analytic discs in ^n

Broader applicability in complex analysis contexts

Abstract

In this paper we generalize Poletsky's classical theorem to a situation where the kernel of Poisson functional is not upper semicontinuous. We give a characterization of thinness of a subset at a point in $\C^n$ in term of analytic discs.