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arXiv · 1607.02244

Rigidity of quasisymmetric mappings on self-affine carpets

Antti Käenmäki·Tuomo Ojala·Eino Rossi
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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.

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Antti Käenmäki, Tuomo Ojala, Eino Rossi. 2016-12-23. Rigidity of quasisymmetric mappings on self-affine carpets. https://doi.org/10.1093/imrn%2Frnw336

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