Conformal Assouad dimension as the critical exponent for combinatorial modulus
Metric Geometry
2023-06-08 v5
Abstract
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.
Cite
@article{arxiv.2209.01187,
title = {Conformal Assouad dimension as the critical exponent for combinatorial modulus},
author = {Mathav Murugan},
journal= {arXiv preprint arXiv:2209.01187},
year = {2023}
}
Comments
46 pages; Definition 3.10 is new and Section 3.4 has been reorginized following a suggestion be the anonymous referee; to appear in Ann. Fenn. Math