%0 Generic %1 ren2023furstenberg %A Ren, Kevin %A Wang, Hong %D 2023 %K fustenberg_conjecture hausdorff_dimension mathematics %T Furstenberg sets estimate in the plane %U http://arxiv.org/abs/2308.08819 %X We fully resolve the Furstenberg set conjecture in $R^2$, that a $(s, t)$-Furstenberg set has Hausdorff dimension $\min(s+t, 3s+t2, s+1)$. As a result, we obtain an analogue of Elekes' bound for the discretized sum-product problem and resolve an orthogonal projection question of Oberlin.

@misc{ren2023furstenberg, 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.}, added-at = {2023-09-10T23:39:48.000+0200}, author = {Ren, Kevin and Wang, Hong}, biburl = {https://www.bibsonomy.org/bibtex/2da5cfebb0a3a03e78a9f822943fbba26/tabularii}, description = {Furstenberg sets estimate in the plane}, interhash = {2af1f1876903d26b5db967b0af81a880}, intrahash = {da5cfebb0a3a03e78a9f822943fbba26}, keywords = {fustenberg_conjecture hausdorff_dimension mathematics}, note = {cite arxiv:2308.08819Comment: 23 pages. v2: fixed small typo in abstract and added more details to arguments, main results unchanged}, timestamp = {2023-09-10T23:39:48.000+0200}, title = {Furstenberg sets estimate in the plane}, url = {http://arxiv.org/abs/2308.08819}, year = 2023 }