Rigidity of quasisymmetric mappings on self-affine carpets

We show that the class of quasisymmetric maps between horizontal self-affine carpets is rigid. Such maps can only exist when the dimensions of the carpets coincide, and in this case, the quasisymmetric maps are quasi-Lipschitz. We also show that horizontal self-affine carpets are minimal for the con...

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Bibliographic Details
Published in:arXiv.org 2016-12
Main Authors: Käenmäki, Antti, Ojala, Tuomo, Rossi, Eino
Format: Article
Language:English
Subjects:
Carpets
Online Access:Get full text
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Summary:We show that the class of quasisymmetric maps between horizontal self-affine carpets is rigid. Such maps can only exist when the dimensions of the carpets coincide, and in this case, the quasisymmetric maps are quasi-Lipschitz. We also show that horizontal self-affine carpets are minimal for the conformal Assouad dimension.
ISSN:2331-8422
DOI:10.48550/arxiv.1607.02244