Uniform domains and quasiconformal mappings on the Heisenberg group
type: Item
instance of: scholarly article
title: Uniform domains and quasiconformal mappings on the Heisenberg group
zbMATH Open document ID: 0824.30011
DOI: 10.1007/BF02567994
author: Luca Capogna
author: Puqi Tang
published in: Manuscripta Mathematica
publication date: 1995-11-13T00:00:00Z
full work available at URL: https://eudml.org/doc/156054
review text: Let \(H\) be the Heisenberg group and \(f: H\to H\) a quasiconformal mapping [\textit{A. Korányi}, \textit{H. M. Reimann}, Foundations for the theory of quasiconformal mappings on the Heisenberg group, Advances in Math. (to appear)]. It is shown that the image of a uniform on an NTA (non- tangentially accessible) domain is again a uniform or an NTA domain. For a study of this phenomenon in \(\mathbb{R}^ n\) see [\textit{O. Martio} and \textit{J. Sarvas}, Ann. Acad. Sci. Fenn., Ser. A I 4, 383-401 (1979; Zbl 0427.30021)]. The proof makes use of the Carnot-Carathéodory distance. Several examples of quasiconformal mappings in \(H\) are constructed with a special attention to volume preserving mappings.
Mathematics Subject Classification ID: 30C65
Mathematics Subject Classification ID: 31B25
zbMATH DE Number: 784029
zbMATH Keywords: quasiconformal mappings
zbMATH Keywords: Heisenberg group
reviewed by: O. Martio
MaRDI profile type: Publication
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OpenAlex ID: W1964077805
description: scientific article; zbMATH DE number 784029