Analytic continuation of biholomorphic maps
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)].
scientific article; zbMATH DE number 4114988