Proper Holomorphic Mappings that must be Rational
Proper Holomorphic Mappings that must be Rational
Suppose/: Dx -» D2 is a proper holomorphic mapping between bounded domains in C".We shall prove that under certain circumstances/must be a rational mapping, i.e., that the n component functions/, of /are rational functions.Theorem 1. Suppose Dx is a bounded domain in C" whose associated Bergman kernel function is a …