Rigidity of quasisymmetric mappings on self-affine carpets
  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. 
Antti K\"aenm\"aki and Tuomo Ojala and Eino Rossi
math.CA