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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{nekrashevych2026conformal,
  title = {{Conformal dimension and self-similar groups}},
  author = {Volodymyr Nekrashevych},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19260},
  eprint = {2610.19260},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19260},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Conformal dimension and self-similar groups
AU  - Volodymyr Nekrashevych
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.19260
UR  - https://arxiv.org/abs/2610.19260
AB  - 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.
ER  -