Domains of holomorphy with edges and lower dimensional boundary singularities

TL;DR

This paper establishes geometric conditions under which domains with edges and boundary singularities are domains of holomorphy, focusing on the measure-theoretic properties of the boundary.

Contribution

It provides necessary and sufficient geometric criteria for domains with edges and singularities to be holomorphically convex, extending classical results to more complex boundary structures.

Findings

Domains with regular boundary points and edges are holomorphy domains under specified conditions.

Zero Hausdorff 1-codimensional measure of the remainder boundary subset is crucial.

The results generalize classical holomorphy criteria to domains with singular boundaries.

Abstract

Necessary and sufficient geometric conditions are given for domains with regular boundary points and edges to be domains of holomorphy provided the remainder boundary subset is of zero Hausdorff 1-codimensional measure.