Rigidity of quasisymmetric mappings on self-affine carpets

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

References in corpus (4)

• Assouad dimension of self-affine carpets
• Weak separation condition, Assouad dimension, and Furstenberg homogeneity
• Local structure of self-affine sets
• Rigidity of fiber-preserving quasisymmetric maps

Cited by in corpus (8)

• On the Assouad dimension of projections
• Dimension of self-affine sets for fixed translation vectors
• Slicing Theorems and rigidity phenomena for self affine carpets
• On the Hausdorff dimension of microsets
• Slices of the Takagi function
• Interpolating with generalized Assouad dimensions
• Dimensions of triangle sets
• Assouad spectrum of Gatzouras-Lalley carpets