University of Oulu

Eino Rossi, Ville Suomala, Fractal Percolation and Quasisymmetric Mappings, International Mathematics Research Notices, Volume 2021, Issue 10, May 2021, Pages 7372–7393,

Fractal percolation and quasisymmetric mappings

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Author: Rossi, Eino1; Suomala, Ville2
Organizations: 1Department of Mathematics and Statistics, University of Helsinki P.O. Box 68 (Pietari Kalmin katu 5) 00014 University of Helsinki, Finland
2Department of Mathematical Sciences, University of Oulu P.O. Box 8000 (Pentti Kaiteran katu 1) FI-90014 University of Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.3 MB)
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Language: English
Published: Oxford University Press, 2021
Publish Date: 2023-01-10


We study the conformal dimension of fractal percolation and show that, almost surely, the conformal dimension of a fractal percolation is strictly smaller than its Hausdorff dimension.

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Series: International mathematics research notices
ISSN: 1073-7928
ISSN-E: 1687-0247
ISSN-L: 1073-7928
Volume: 2021
Issue: 10
Pages: 7372 - 7393
DOI: 10.1093/imrn/rnaa040
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: This work was supported by CONICET [to E.R.]; the Finnish Academy of Science and Letters [to E.R.]; Mittag–Leffler institute[to E.R.]; the University of Helsinki via the project Quantitative rectifiability of sets and measures in Euclidean Spaces and Heisenberg groups [project No.7516125 to E.R.]; Academy of Finland CoE in Analysis and Dynamics research [to V.S.]. We thank the Mittag–Leffler institute and the organizers of the Fractal Geometry and Dynamics program, where this project started. VS also acknowledges the Finnish Academy of Science and Letters for covering the costs of the visit.
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