A remark on the relative extremal function

TL;DR

This paper presents an annulus formula for the relative extremal function in Stein spaces, which could facilitate the extension of separately holomorphic functions on complex cross structures.

Contribution

It introduces a new annulus formula for the relative extremal function in Stein spaces, advancing the understanding of function extension in complex analysis.

Findings

Derived an annulus formula for the relative extremal function

Potential applications in extending separately holomorphic functions

Provides theoretical tools for Stein space analysis

Abstract

The main result of this paper is some "annulus" formula for the relative extremal function in the context of Stein spaces (Theorem 1.1). Our result may be useful in the theory of the extension of separately holomorphic functions on generalized (N,k)-crosses lying in the product of Stein manifolds (Theorem 4.6).