Conformal Assouad dimension as the critical exponent for combinatorial modulus

Kirjoittajat

  • Mathav Murugan University of British Columbia, Department of Mathematics

Avainsanat:

Conformal gauge, power quasisymmetry, Assouad dimension

Abstrakti

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.

 

Osasto
Articles

Julkaistu

2023-07-02

Viittaaminen

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