Metric quasiconformality and Sobolev regularity in non-Ahlfors regular spaces

Given a homeomorphism between -dimensional spaces , we show that satisfying the metric definition of quasiconformality outside suitable exceptional sets implies that belongs to the Sobolev class , where , and also implies one direction of the geometric definition of quasiconformality. Unlike previou...

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Bibliographic Details
Published inAnalysis and Geometry in Metric Spaces Vol. 12; no. 1; pp. 554 - 577
Main Authors Lahti, Panu, Zhou, Xiaodan
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 18.04.2024
De Gruyter Poland
Subjects
30C65
30L10
46E36
absolute continuity
Ahlfors regularity
Lie groups
modulus of a curve family
Newton-Sobolev mapping
quasiconformal mapping
Regularity
Topology
weighted space
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Summary:Given a homeomorphism between -dimensional spaces , we show that satisfying the metric definition of quasiconformality outside suitable exceptional sets implies that belongs to the Sobolev class , where , and also implies one direction of the geometric definition of quasiconformality. Unlike previous results, we only assume a pointwise version of Ahlfors -regularity, which in particular enables various weighted spaces to be included in the theory. Notably, even in the classical Euclidean setting, we are able to obtain new results using this approach. In particular, in spaces including the Carnot groups, we are able to prove the Sobolev regularity without the strong assumption of the infinitesimal distortion belonging to
ISSN:2299-3274
2299-3274
DOI:10.1515/agms-2024-0001