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Furstenberg sets estimate in the plane (2308.08819v3)
Published 17 Aug 2023 in math.CA, math.CO, and math.MG
Abstract: We fully resolve the Furstenberg set conjecture in $\mathbb{R}2$, that a $(s, t)$-Furstenberg set has Hausdorff dimension $\ge \min(s+t, \frac{3s+t}{2}, s+1)$. As a result, we obtain an analogue of Elekes' bound for the discretized sum-product problem and resolve an orthogonal projection question of Oberlin.