Applications holomorphes propres entre domaines à bord analytique réel. (Proper holomorphic mappings between real-analytic domains). (French) Zbl 0656.32013

Let D and D’ be bounded domains in \({\mathbb{C}}^ n\) with smooth real- analytic boundaries, and let f: \(D\to D'\) be a proper holomorphic map. The authors prove that if D and D’ are algebraic, f is biholomorphic, and \(n=2\), then f extends holomorphically to a neighborhood of \(\bar D.\) In addition, if \(n\geq 3\), then every proper holomorphic mapping f: \(D\to D'\) between bounded algebraic domains extends continuous to \(\bar D.\)
Reviewer: R.Aron


32D15 Continuation of analytic objects in several complex variables
32H35 Proper holomorphic mappings, finiteness theorems
32C05 Real-analytic manifolds, real-analytic spaces