An improved bound for the dimension of -Furstenberg sets
Kornélia Héra
The University of Chicago, USAPablo Shmerkin
Universidad Torcuato Di Tella, Ciudad de Buenos Aires, ArgentinaAlexia Yavicoli
The University of British Columbia, Vancouver, Canada
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Abstract
We show that given there is a constant such that any planar -Furstenberg set has Hausdorff dimension at least . This improves several previous bounds, in particular extending a result of Katz–Tao and Bourgain. We follow the Katz–Tao approach with suitable changes, along the way clarifying, simplifying and/or quantifying many of the steps.
Cite this article
Kornélia Héra, Pablo Shmerkin, Alexia Yavicoli, An improved bound for the dimension of -Furstenberg sets. Rev. Mat. Iberoam. 38 (2022), no. 1, pp. 295–322
DOI 10.4171/RMI/1281