An improved bound for the dimension of (α, 2α)-Furstenberg sets
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We show that given α e (0, 1) there is a constant c = c α > 0 such that any planar (α, 2α)-Furstenberg set has Hausdorff dimension at least 2α + 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.
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Kornélia Héra, Pablo Shmerkin, Alexia Yavicoli, An improved bound for the dimension of (\alpha,2\alpha)(α,2α)-Furstenberg sets. Rev. Mat. Iberoam. 38 (2022), no. 1, pp. 295–322