Proper holomorphic self-mappings of Hartogs domains in \(\mathbb{C}^ 2\)
type: Item
instance of: scholarly article
title: Proper holomorphic self-mappings of Hartogs domains in \(\mathbb{C}^ 2\)
zbMATH Open document ID: 0790.32002
author: Xiaojun Huang
author: Yifei Pan
published in: Michigan Mathematical Journal
publication date: 1994-06-20T00:00:00Z
review text: The authors identify a class of bounded pseudoconvex Hartogs domains in \(\mathbb{C}^ 2\) for which any proper holomorphic self-map must be biholomorphic. The domains have the form \(\Omega=\{(z,w)\in\mathbb{C}^ 2\mid| w|^ 2+\varphi(z)<0\}\) with \(\varphi(z)\) a smooth function; the set where the Levi determinant vanishes can have no interior limit points in the intersection of \(\Omega\) with the \(z\) plane, and at weakly pseudoconvex boundary points either the Levi determinant vanishes to finite order or else \({\partial^ k\varphi\over\partial z^ k}(z_ 0)=0\) for all integers \(k>0\).
Mathematics Subject Classification ID: 32A07
Mathematics Subject Classification ID: 32H35
zbMATH DE Number: 474966
zbMATH Keywords: proper holomorphic maps
zbMATH Keywords: Hartogs domains
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029004748
OpenAlex ID: W2040873960
DOI: 10.1307/MMJ/1029004748
description: scientific article; zbMATH DE number 474966