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arXiv · 2006.06833

An improved result for Falconer's distance set problem in even dimensions

Xiumin Du·Alex Iosevich·Yumeng Ou·Hong Wang·Ruixiang Zhang
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Abstract

We show that if compact set $E\subset \mathbb{R}^d$ has Hausdorff dimension larger than $\frac{d}{2}+\frac{1}{4}$, where $d\geq 4$ is an even integer, then the distance set of $E$ has positive Lebesgue measure. This improves the previously best known result towards Falconer's distance set conjecture in even dimensions.

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Xiumin Du, Alex Iosevich, Yumeng Ou, Hong Wang, Ruixiang Zhang. 2020-06-11. An improved result for Falconer's distance set problem in even dimensions. https://arxiv.org/abs/2006.06833

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