Conformal Assouad dimension as the critical exponent for combinatorial modulus
Keywords:Conformal gauge, power quasisymmetry, Assouad dimension
AbstractThe conformal Assouad dimension is the infimum of all possible values of Assouad dimension after a quasisymmetric change of metric. We show that the conformal Assouad dimension equals a critical exponent associated to 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. We also show that the value of conformal Assouad dimension is unaffected if we replace quasisymmetry with power quasisymmetry in its definition.
How to Cite
Murugan, M. (2023). Conformal Assouad dimension as the critical exponent for combinatorial modulus. Annales Fennici Mathematici, 48(2), 453–491. https://doi.org/10.54330/afm.131478
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