Conformal dimension of Bedford-McMullen carpets

We show that the Hausdorff dimension of a Bedford-McMullen carpet with non-uniform fibres can be lowered with a quasisymmetry, provided that the defining iterated function system does not have a full column. We prove this by constructing explicit dimension lowering metrics which are quasisymmetrically equivalent to the Euclidean metric.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-11-02
DOI
https://doi.org/10.48550/arxiv.2611.03252
Primary Topic
Mathematical Dynamics and Fractals
Type
preprint
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preprint

Conformal dimension of Bedford-McMullen carpets

Roope Anttila
arXiv (Cornell University)
Mathematical Dynamics and Fractals
preprint

Conformal dimension of Bedford-McMullen carpets

Roope Anttila
preprint en

Abstract

We show that the Hausdorff dimension of a Bedford-McMullen carpet with non-uniform fibres can be lowered with a quasisymmetry, provided that the defining iterated function system does not have a full column. We prove this by constructing explicit dimension lowering metrics which are quasisymmetrically equivalent to the Euclidean metric.

arXiv (Cornell University)
Mathematical Dynamics and Fractals
DOIOpen Access PDFOpenAlex
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Conformal dimension of Bedford-McMullen carpets — Roope Anttila · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS