An approximate Riemann mapping theorem in \({\mathbb{C}}^ n\)
type: Item
instance of: scholarly article
title: An approximate Riemann mapping theorem in \({\mathbb{C}}^ n\)
zbMATH Open document ID: 0579.32041
DOI: 10.1007/BF01458582
published in: Mathematische Annalen
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164132
review text: Let \(T_ 0(n)\) be the class of all domains in \({\mathbb{C}}^ n\) diffeomorphic to the unit ball. The following theorem is proved. For any two domains \(G_ i\in T_ 0(n)\) and compacts \(K_ i\subset G_ i\), \(i=1,2\) there exist a domain \(D\in T_ 0(n)\) and two biholomorphic imbeddings \(F_ i: D\to G_ i\) such that \(F_ i(D)\supset K_ i\), \(i=1,2.\) The domain D in this theorem is constructed independently of \(G_ i\) and \(K_ i.\) The paper contains also an example of a diffeomorphism class for which the statement of the theorem does not hold.
Mathematics Subject Classification ID: 32H99
Mathematics Subject Classification ID: 30C25
Mathematics Subject Classification ID: 32A30
Mathematics Subject Classification ID: 14E25
zbMATH DE Number: 3927370
zbMATH Keywords: unit ball
zbMATH Keywords: biholomorphic imbeddings
zbMATH Keywords: approximate Riemann mapping theorem in \({\mathbb{C}}^ n\)
author: Buma Fridman
MaRDI profile type: Publication
cites work: Extremal Holomorphic Imbeddings Between the Ball and Polydisc
cites work: Proper holomorphic mappings
cites work: Deformations of strictly pseudoconvex domains
cites work: A Universal Exhausting Domain
cites work: Q5815752
cites work: Deformation of complex structures, estimates for the (partial d) equation, and stability of the Bergman kernel
cites work: Q3924489
cites work: A note on mapping polydiscs into balls and vice versa
cites work: Q3958740
description: scientific article; zbMATH DE number 3927370