An elementary proof of the cross theorem in the Reinhardt case

TL;DR

This paper provides an elementary proof of the cross theorem specifically for Reinhardt domains, highlighting the connection between their holomorphic properties and the convex geometry of their logarithmic images.

Contribution

It offers a simplified, elementary proof of the cross theorem in the Reinhardt domain case, emphasizing geometric relationships.

Findings

The proof is elementary and accessible.

Reveals the link between holomorphic geometry and convex geometry.

Clarifies the structure of Reinhardt domains in complex analysis.

Abstract

We present an elementary proof of the cross theorem in the case of Reinhardt domains. The results illustrates the well-known interrelations between the holomorphic geometry of a Reinhardt domain and the convex geometry of its logarithmic image.