Proper holomorphic maps between complete reinhardt domains in

Abstract

Let D and D′ be two bounded complete Reinhardt domains in and let F: D → D′ be a proper holomorphic mapping. We prove that if D or D′ is not a generalized pseudoellipsoid, then there exist two bidiscs δ ⊆ D and δ′ ⊇ D′ such that F restricts to a proper holomorphic map F δ → δ ′. From this it is deduced that, if D ≠ δ F is always of the form F(z1,z2)= (Az m π(1), Bzn π(2)), where π is a permutation of {1,2}. This fact brings to the complete classification of all proper mans between bounded complete: Reinhardt domains in .