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Proper holomorphic mappings between real-analytic pseudoconvex domains in \({\mathbb{C}}^ n\). (English) Zbl 0661.32025

The authors provide a “simple proof” that a proper holomorphic mapping between pseudoconvex domains D and D’ of \({\mathbb{C}}^ n\) with real- analytic boundaries extends to a proper holomorphic map between neighborhoods of the closures of D and D’. Although the authors describe the proof as “simple”, their arguments are technically rather involved. Heavy use is made of the implicit function theorem and formal power series techniques, as well as, the idea of “complexification of a real hypersurface” as developed by S. Webster, to whom the authors give special credit.
Reviewer: G.Harris

MSC:

32V40 Real submanifolds in complex manifolds
32H35 Proper holomorphic mappings, finiteness theorems
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References:

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