Reflection principle in higher dimensions
type: Item
instance of: scholarly article
title: Reflection principle in higher dimensions
zbMATH Open document ID: 0914.32008
author: S. I. Pinchuk
author: K. Diederich
published in: Documenta Mathematica
publication date: 1998-08-06T00:00:00Z
full work available at URL: https://eudml.org/doc/222868
full work available at URL: Pinchuk.MAN.html
review text: 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 \(z^0\).
Mathematics Subject Classification ID: 32H40
Mathematics Subject Classification ID: 32D15
Mathematics Subject Classification ID: 32H99
Mathematics Subject Classification ID: 32H35
zbMATH DE Number: 1184304
zbMATH Keywords: proper holomorphic maps
zbMATH Keywords: reflection principle
zbMATH Keywords: Segre varieties
zbMATH Keywords: holomorphic correspondences
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1184304