Conformal Assouad dimension as the critical exponent for combinatorial modulus

2022/09/02 by Mathav Murugan, Murugan, Mathav · 1 citation
Mathematics · #30L10 #51F99 #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2209.01187

openalex publication_date 2022/09/02 · openalex created_date 2022/09/06 · openalex updated_date 2026/07/28

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.

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