Conformal Assoaud dimension as the critical exponent for combinatorial modulus
December 7, 2022
Vancouver, V6T 1Z2Canada
The conformal Assouad dimension is the infimum of all possible values of the Assouad dimension after a quasisymmetric change of metric. We show that the conformal Assouad dimension equals a critical exponent associated with the combinatorial modulus for any compact doubling metric space. This generalizes a similar result obtained by Carrasco Piaggio for the Ahlfors regular conformal dimension to a larger family of spaces.