A new Hartogs type extension results for the cross-like objects

TL;DR

This paper explores advanced extension theorems for holomorphic functions on cross-like structures, generalizing Hartogs' theorem and examining envelopes of holomorphy through extremal functions.

Contribution

It introduces new Hartogs-type extension results for cross-like objects and investigates their envelopes of holomorphy using extremal functions.

Findings

Extended Hartogs theorem to more general cross-like structures

Characterized envelopes of holomorphy via extremal functions

Provided conditions for the existence of 'nice' descriptions of envelopes

Abstract

We discuss the problem of the existence of envelopes of holomorphy of the A-crosses, which leads us to the far-reaching generalizations of the famous Hartogs theorem. We also take under consideration the issue of the existence of "nice" general descriptions of envelopes of holomorphy of the cross-like objects in terms of the relative extremal function, which seems to be very natural in the light of the extension theory of separately holomorphic functions on classical crosses and (N,k)-crosses.