Reflection principle in higher dimensions
The article discusses the use of the reflection principle in studying the following conjecture: Let \(D,D'\subset\subset\mathbb C^n\) be domains, \(n\geq 2\). Suppose that \(z^0 \in \partial D\) and \({z'}^0 \in \partial D'\) have open neighborhoods \(W\) resp. \(W'\) such that \(\partial D \cap W\) and \(\partial D' \cap W'\) are smooth real-analytic, essentially finite hypersurfaces and let \(f : D \to D'\) be a proper holomorphic map. Furthermore, suppose, that the given map \(f\) extends as a proper holomorphic correspondence \(F\) to a neighborhood of \(z^0\) such that \(\widehat F(z^0) = {z'}^0\). Then the map \(f\) extends holomorphically to a neighborhood of \(z^0\).
scientific article; zbMATH DE number 1184304