Rigidity of Quasisymmetric Mappings on Self-affine Carpets
Abstract
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.
Main Authors
Format
Articles
Research article
Published
2018
Series
Subjects
Publication in research information system
Publisher
Oxford University Press
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201806143219Use this for linking
Review status
Peer reviewed
ISSN
1073-7928
DOI
https://doi.org/10.1093/imrn/rnw336
Language
English
Published in
International Mathematics Research Notices
Citation
- Käenmäki, A., Ojala, T., & Rossi, E. (2018). Rigidity of Quasisymmetric Mappings on Self-affine Carpets. International Mathematics Research Notices, 2018(12), 3769-3799. https://doi.org/10.1093/imrn/rnw336
License
Copyright© The Author(s) 2017. Published by Oxford University Press. All rights reserved.