Rigidity of quasisymmetric mappings on self-affine carpets
Classical Analysis and ODEs
2018-06-27 v3
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.
Cite
@article{arxiv.1607.02244,
title = {Rigidity of quasisymmetric mappings on self-affine carpets},
author = {Antti Käenmäki and Tuomo Ojala and Eino Rossi},
journal= {arXiv preprint arXiv:1607.02244},
year = {2018}
}
Comments
20 pages, 4 figures