$L_h^2$-domains of holomorphy and the Bergman kernel

TL;DR

This paper characterizes $L_h^2$-domains of holomorphy by analyzing the boundary behavior of the Bergman kernel and geometric boundary properties.

Contribution

It provides a new characterization of $L_h^2$-domains of holomorphy using boundary analysis of the Bergman kernel and geometric boundary features.

Findings

Boundary behavior of the Bergman kernel characterizes $L_h^2$-domains

Geometric boundary properties are key to the characterization

New criteria for identifying $L_h^2$-domains of holomorphy

Abstract

We give a characterization of $L_h^2$-domains of holomorphy with the help of the boundary behavior of the Bergman kernel and geometric properties of the boundary, respectively.