Proper holomorphic mappings in the special class of Reinhardt domains

TL;DR

This paper provides a complete characterization of proper holomorphic mappings between specific pseudoconvex Reinhardt domains in ^2, focusing on those with logarithmic images being a strip or a half-plane.

Contribution

It offers a new, comprehensive description of proper holomorphic mappings in a special class of Reinhardt domains with particular geometric properties.

Findings

Characterization of proper holomorphic mappings for domains with logarithmic images as strips or half-planes.

Identification of conditions under which these mappings exist and their explicit forms.

Extension of understanding of holomorphic mappings in complex analysis and geometric function theory.

Abstract

A complete characterization of proper holomorphic mappings between domains from the class of all pseudoconvex Reinhardt domains in $\C^2$ with the logarithmic image equal to a strip or a half-plane is given.