An improved bound for the dimension of $(\alpha,2\alpha)$-Furstenberg sets

We show that given [alpha] [member of] (0,1) there is a constant c = c([alpha]) > 0 such that any planar ([alpha], 2[alpha])-Furstenberg set has Hausdorff dimension at least 2a + c. This improves several previous bounds, in particular extending a result of Katz-Tao and Bourgain. We follow the Kat...

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Published inRevista matemática iberoamericana Vol. 38; no. 1; pp. 295 - 322
Main Authors Hera, Kornelia, Shmerkin, Pablo, Yavicoli, Alexia
Format Journal Article
LanguageEnglish
Published European Mathematical Society Publishing House 01.01.2022
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Canadá
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Summary:We show that given [alpha] [member of] (0,1) there is a constant c = c([alpha]) > 0 such that any planar ([alpha], 2[alpha])-Furstenberg set has Hausdorff dimension at least 2a + c. 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.
ISSN:0213-2230
2235-0616
DOI:10.4171/RMI/1281