Proper holomorphic mappings in some class of unbounded domains

Abstract

In the paper the problem of the form of proper holomorphic mappings between elementary Reinhardt domains of the rational type in C² is solved. The pluricomplex Green function with many poles is used in the solution of the problem. Additionally, we solve the holomorphic equivalence problem of elementary Reinhardt domains of the arbitrary type in Cⁿ The results in the paper are generalizations of those from two papers of S. Shimizu.