Rigidity of Quasisymmetric Mappings on Self-affine Carpets
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
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International Mathematics Research NoticesDate
2018Copyright
© The Author(s) 2017. Published by Oxford University Press. All rights reserved.
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.
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Oxford University PressISSN Search the Publication Forum
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