Extremal length for quasiregular mappings on Heisenberg groups.
type: Item
instance of: scholarly article
title: Extremal length for quasiregular mappings on Heisenberg groups.
zbMATH Open document ID: 1094.30024
DOI: 10.1016/S0022-247X(03)00350-0
author: Irina Markina
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-09-07T00:00:00Z
review text: In 1957 \textit{B. Fuglede} [Acta. Math. 98, 171--219 (1957; Zbl 0079.27703)] has introduced a notion of the system of exceptional measures. A system of measures \(E\) is said to be exceptional of order \(p\) if its \(p\)-modulus \(M_p(E)\) vanishes. \textit{E. Poletskiĭ} [Mat. Sb., N. Ser. 83(125), 261--272 (1970; Zbl 0207.37603)] was the first who applied this notion to a description of the behavior of a family of curves under a quasiregular mapping (in another terminology a mapping with bounded distortion) in \(\mathbb R^n\). In the present paper we study the behavior of horizontal curves under contact maps and the modulus of a family of horizontal curves under a quasiregular mapping on the Heisenberg group \(\mathbb H^n\).
Mathematics Subject Classification ID: 30C65
Mathematics Subject Classification ID: 43A80
zbMATH DE Number: 1976009
zbMATH Keywords: Quasiregular mapping
zbMATH Keywords: Heisenberg group
zbMATH Keywords: Carnot--Carathéodory metric
zbMATH Keywords: \(p\)-modulus of a family of curves
MaRDI profile type: Publication
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full work available at URL: s0022-247x(03)00350-0
OpenAlex ID: W2163475642
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description: scientific article; zbMATH DE number 1976009