Extension of proper holomorphic mappings past the boundary
type: Item
instance of: scholarly article
title: Extension of proper holomorphic mappings past the boundary
zbMATH Open document ID: 0583.32044
DOI: 10.1007/BF01168824
published in: Manuscripta Mathematica
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155047
review text: The authors prove that a proper holomorphic map \(f: \Omega\to D\) between bounded pseudoconvex domains in \({\mathbb{C}}^ n\) with real analytic boundaries extends to be holomorphic in a neighbourhood of \({\bar \Omega}\) if either (1) \(\Omega\) and D are defined by real polynomials or (2) D satisfies ''condition Q'' (i.e. the Bergman projection associated to D maps \(C_ 0^{\infty}(D)\) into \(H(\bar D)\), for instance if D is strictly pseudoconvex, if D is a complete Reinhardt domain, or if the \({\bar \partial}\)-Neumann problem for D is globally analytic hypoelliptic). Main tools are extension of holomorphic correspondences and a transformation rule for the Bergman projection under correspondences. Consequence: If D is a simply connected strictly pseudoconvex domain in \({\mathbb{C}}^ n\) with real analytic boundary, an irreducible proper holomorphic self correspondence of D is an automorphism of D.
Mathematics Subject Classification ID: 32E35
Mathematics Subject Classification ID: 32D15
Mathematics Subject Classification ID: 32H35
Mathematics Subject Classification ID: 32T99
zbMATH DE Number: 3933466
zbMATH Keywords: extension past the boundary
zbMATH Keywords: proper holomorphic map
zbMATH Keywords: bounded pseudoconvex domains
zbMATH Keywords: Bergman projection
zbMATH Keywords: holomorphic correspondences
author: Eric Bedford
author: Steven R. Bell
reviewed by: Cabiria Andreian Cazacu
MaRDI profile type: Publication
cites work: Q3728366
cites work: Analytic hypoellipticity of the (partial-d-bar)-Neumann problem and extendability of holomorphic mappings
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cites work: ON THE ANALYTIC CONTINUATION OF HOLOMORPHIC MAPPINGS
OpenAlex ID: W2006081283
description: scientific article; zbMATH DE number 3933466