Proper holomorphic mapppings between Reinhardt domains in $\mathbb C^2$

TL;DR

This paper classifies all non-elementary proper holomorphic maps between non-hyperbolic Reinhardt domains in complex two-dimensional space, providing a comprehensive understanding of their existence conditions.

Contribution

It offers a complete description of when such proper holomorphic maps exist between these specific Reinhardt domains, advancing the understanding of complex mappings in several complex variables.

Findings

Characterization of existence conditions for proper holomorphic maps

Identification of all non-elementary mappings between non-hyperbolic Reinhardt domains

Clarification of the relationship between domain pairs and mapping properties

Abstract

We describe all possibilities of existence of non-elementary proper holomorphic maps between non-hyperbolic Reinhardt domains in $\mathbb C^2$ and the corresponding pairs of domains.