Proper holomorphic mappings between Reinhardt domains in \(\mathbb C^{2}\) (Q846228)

The main result of the paper is the description of non-elementary proper holomorphic mappings between non-hyperbolic Reinhardt domains in \(\mathbb C^2\) as well as the corresponding pairs of domains: the author shows that one of two possible scenarios has to take place. It is a generalization of \textit{A. V. Isaev} and \textit{N. G. Kruzhilin} [Mich. Math. J. 54, 33--64 (2006; Zbl 1122.32011)] result to unbounded domains, except for the case of domains whose logarithmic images of envelopes of holomorphy are equal to \(\mathbb R^2\). The author also obtains some partial results for proper maps between domains of the form \(\mathbb C^2_*\), \(\mathbb C^2\), and \(\mathbb C\times\mathbb C_*\).