Rigidity of quasisymmetric mappings on self-affine carpets
arXiv:1607.02244 · doi:10.1093/imrn/rnw336
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.
20 pages, 4 figures