Analytic continuation of biholomorphic maps
type: Item
instance of: scholarly article
title: Analytic continuation of biholomorphic maps
zbMATH Open document ID: 0681.32010
author: Eric Bedford
author: S. I. Pinchuk
published in: Michigan Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: The authors give a fairly simple geometric proof of the following theorem of \textit{M. S. Baouendi}, \textit{H. Jacobowitz} and \textit{F. Treves} [Ann. Math., II. Ser. 122, 365-400 (1985; Zbl 0583.32021)]: Let f: \(\Omega_ 1\to \Omega_ 2\) be a biholomorphic map between domains in \({\mathbb{C}}^ n\) with real analytic boundary which extends to a diffeomorphism of the closures. If \(p\in b\Omega_ 1\) and if there is no nontrivial analytic variety contained in \(b\Omega_ 2\) through f(p), then f extends holomorphically to p. The main point is to show that at (p,f(p)) the graph of f is contained in the germ of an analytic variety. The conclusion then follows from an earlier result of the first author and \textit{S. Bell} [Manuscr. Math. 50, 1-10 (1985; Zbl 0583.32044)].
Mathematics Subject Classification ID: 32D15
Mathematics Subject Classification ID: 32H99
zbMATH DE Number: 4114988
zbMATH Keywords: analytic continuation
zbMATH Keywords: biholomorphic map
reviewed by: R. Michael Range
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029003820
OpenAlex ID: W2076371309
DOI: 10.1307/MMJ/1029003820
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description: scientific article; zbMATH DE number 4114988