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PreprintCC BY-NC-SA 4.0arXiv

Conformal dimension of Bedford-McMullen carpets

  • Roope Anttila
Open at sourcePDFDOICite

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.

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Cite

BibTeXRIS
BibTeX
@misc{anttila2026conformal,
  title = {{Conformal dimension of Bedford-McMullen carpets}},
  author = {Roope Anttila},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.03252},
  eprint = {2611.03252},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.03252},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Conformal dimension of Bedford-McMullen carpets
AU  - Roope Anttila
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.03252
UR  - https://arxiv.org/abs/2611.03252
AB  - 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.
ER  -