Quasiregular mappings of the Heisenberg group
type: Item
instance of: scholarly article
title: Quasiregular mappings of the Heisenberg group
zbMATH Open document ID: 0754.30018
DOI: 10.1007/BF01934345
author: Ilkka Holopainen
author: Seppo Rickman
published in: Mathematische Annalen
publication date: 1993-01-12T00:00:00Z
full work available at URL: https://eudml.org/doc/165021
review text: A Picard type theorem is proved for quasiregular maps of the \((2m+1)\)- dimensional Heisenberg group \(H_ m\) into \((2m+1)\)-manifolds \(M=N\backslash\{a_ 1,\dots,a_ q\}\), where \(N\) is compact and \(M\) is given an arbitrary Riemannian metric. Surprisingly, there exists a nonconstant quasiregular map of \(H_ 1\) into \(\mathbb{R}^ 3\backslash\{0\}\), and consequently of \(H_ 1\) into \(\mathbb{R}^ 3\backslash\{a_ 1,\dots,a_ q\}\) when earlier constructions are combined, but there exists no such map of \(H_ m\) into \(H_ m\backslash\{a\}\), \(a\in H_ m\).
Mathematics Subject Classification ID: 30C65
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 86219
zbMATH Keywords: Picard type theorem
zbMATH Keywords: quasiregular maps
zbMATH Keywords: Heisenberg group
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 86219