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arXiv · 2610.19260

Conformal dimension and self-similar groups

Volodymyr Nekrashevych
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Abstract

We study the Ahlfors-regular conformal dimension of spaces with locally expanding self-covering maps and, more generally, limit spaces of contracting self-similar groups. We show that the conformal dimension is characterized by combinatorial moduli associated with the Schreier graphs of these groups. We compare these moduli with contraction coefficients of self-similar group actions and with algebras of functions on the limit spaces satisfying asymptotic $p$-energy conditions. We also give conditions on the group when the conformal dimension is equal to the infimum of visual metrics on the self-similarity complex.

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Volodymyr Nekrashevych. 2026-10-13. Conformal dimension and self-similar groups. https://arxiv.org/abs/2610.19260

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