K. Ren, and H. Wang. (2023)cite arxiv:2308.08819Comment: 23 pages. v2: fixed small typo in abstract and added more details to arguments, main results unchanged.
Abstract
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.
%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
}