Geodesic
Conformal Assouad dimension as the critical exponent for combinatorial modulus
Mathav Murugan1
1University of British Columbia, Department of Mathematics
Annales Fennici Mathematici, Tome 48 (2023) no. 2, pp. 453-491

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The 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.  
DOI : 10.54330/afm.131478
Keywords: Conformal gauge, power quasisymmetry, Assouad dimension

Mathav Murugan  1

1 University of British Columbia, Department of Mathematics 
Mathav Murugan. Conformal Assouad dimension as the critical exponent for combinatorial modulus. Annales Fennici Mathematici, Tome 48 (2023) no. 2, pp. 453-491. doi: 10.54330/afm.131478
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