A remark on quasiconformal mappings on Carnot groups
type: Item
instance of: scholarly article
title: A remark on quasiconformal mappings on Carnot groups
zbMATH Open document ID: 0898.22006
published in: Michigan Mathematical Journal
publication date: 1998-11-01T00:00:00Z
review text: A. Koranyi and M. Reimann informed me that a result of theirs on the theory of quasiconformal mappings on the Heisenberg groups contradicted inequality (20.17) in my monograph [Strong rigidity of locally symmetric spaces, Ann. Math. Studies, No. 78 (Princeton 1973; Zbl 0265.53039)] which is asserted there without proof and used in the proof of Proposition 21.3. Proposition 21.3 is an essential step in proving strong rigidity for locally hyperbolic spaces. This paper offers a correction of the proof of Proposition 21.3 via bypassing the faulty inequality (20.17). The method used can be generalized directly to simplify the definition of quasiconformal mappings on two-step Carnot groups.
Mathematics Subject Classification ID: 22E40
Mathematics Subject Classification ID: 30C65
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 575618
zbMATH Keywords: quasiconformal mappings
zbMATH Keywords: Heisenberg groups
zbMATH Keywords: strong rigidity
zbMATH Keywords: locally hyperbolic spaces
zbMATH Keywords: two-step Carnot groups
author: G. Daniel Mostow
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029004912
OpenAlex ID: W2035756777
DOI: 10.1307/MMJ/1029004912
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description: scientific article; zbMATH DE number 575618