Proper holomorphic mappings between complex ellipsoids and generalized Hartogs triangles

TL;DR

This paper explicitly characterizes proper holomorphic mappings between complex ellipsoids and generalized Hartogs triangles, including their automorphism groups, advancing understanding of complex domain mappings.

Contribution

It provides explicit forms of proper holomorphic mappings and characterizes their existence between complex ellipsoids and generalized Hartogs triangles, including automorphism groups.

Findings

Explicit forms of proper holomorphic mappings between complex ellipsoids.

Characterization of existence of mappings between generalized Hartogs triangles.

Determination of automorphism groups for these domains.

Abstract

The explicit form of proper holomorphic mappings between complex ellipsoids is given. Using this description, we characterize the existence of proper holomorphic mappings between generalized Hartogs triangles and give their explicit form. In particular, the automorphism group of such domains is found.