Proper holomorphic mappings between generalized Hartogs triangles

TL;DR

This paper characterizes proper holomorphic mappings between generalized Hartogs triangles, providing explicit forms, describing automorphism groups, and proving rigidity of self-mappings, thus answering key open questions in several complex variables.

Contribution

It fully characterizes proper holomorphic mappings between generalized Hartogs triangles and describes their automorphism groups, advancing understanding of these complex domains.

Findings

Explicit forms of proper holomorphic mappings derived

Automorphism groups of generalized Hartogs triangles characterized

Rigidity of proper holomorphic self-mappings established

Abstract

Answering all questions---concerning proper holomorphic mappings between generalized Hartogs triangles---posed by Jarnicki and Plfug (First steps in several complex variables: Reinhardt domains, 2008) we characterize the existence of proper holomorphic mappings between generalized Hartogs triangles and give their explicit form. In particular, we completely describe the group of holomorphic automorphisms of such domains and establish rigidity of proper holomorphic self-mappings on them.