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arXiv · 2308.08819

Furstenberg sets estimate in the plane

Kevin Ren·Hong Wang
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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.

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Kevin Ren, Hong Wang. 2023-08-17. Furstenberg sets estimate in the plane. https://arxiv.org/abs/2308.08819

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