Serre problem for unbounded pseudoconvex Reinhardt domains in $\mathbb C^2$

TL;DR

This paper characterizes non-hyperbolic pseudoconvex Reinhardt domains in complex two-dimensional space where the Serre problem has a positive answer, advancing understanding of complex analysis in these domains.

Contribution

It provides a complete characterization of certain pseudoconvex Reinhardt domains in a7^2 related to the Serre problem, which was previously not fully understood.

Findings

Identifies conditions under which the Serre problem is positive for these domains

Clarifies the relationship between hyperbolicity and the Serre problem in Reinhardt domains

Advances the classification of pseudoconvex Reinhardt domains in complex analysis

Abstract

A characterization of non-hyperbolic pseudoconvex Reinhardt domains in $\mathbb C^2$ for which the answer to the Serre problem is positive is given.