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

Diederich, Klas; Fornaess, John E.

C. R. Acad. Sci., Paris, Sér. I 307, No. 7, 321-324 (1988).

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

MSC:

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

Keywords:

analytic extension; proper holomorphic mapping; bounded algebraic domains