Proper holomorphic mappings in some class of unbounded domains

Abstract

In the paper the problem of the form of proper holomorphic mappings between elementary Remhardt domains of the rational type in C 2 is solved.The pluncomplex Green function with many poles is used in the solution of the problem.Additionally, we solve the holomorphic equivalence problem of elementary Remhardt domains of the arbitrary type in C" The results in the paper are generalizations of those from two papers of S. Shimizu. PEPIt is also well-known that ^(P; v; •) e C/f D P v .Put Vo := {z = (z 1? ... ,z Λ ) e C n : z x z n = 0}.Let α = (αi,..., ct») e (R+) n , where n > 1 (Jf+ stands for positive numbers).Define