Furstenberg sets estimate in the plane

By K. Ren, Hong Wang. 2023

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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.

View Paper: https://www.semanticscholar.org/paper/9368d701a8ccf3a035fbd1c1dd269dff50a3aaa7