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Proper holomorphic mappings. (English) Zbl 0534.32009

This is a survey of some recent results on proper mappings \(f:\Omega \to D\) in the case where \(\Omega\), \(D\subset \subset {\mathbb{C}}^ n\) are bounded domains with smooth boundary. The main attention is given to the boundary smoothness of f and of the branch locus of f. - The case \(\dim \Omega<\dim D\) is more complicated than the equidimensional case. Some partial results and open problems are discussed for mappings into higher dimensional spaces.

MSC:

32H99 Holomorphic mappings and correspondences
32E35 Global boundary behavior of holomorphic functions of several complex variables
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