New improvement to Falconer distance set problem in higher dimensions

Xiumin Du, Yumeng Ou, Kevin Ren +1

We show that if a compact set $E\subset {\mathbb{R}}^d$ has Hausdorff dimension larger than $\frac{d}{2}+\frac{1}{4}-\frac{1}{8d+4}$, where $d\ge 3$, then there is a point $x\in E$…