An elementary approach to simplexes in thin subsets of Euclidean space

Allan Greenleaf, Alex Iosevich, Bochen Liu +1

We prove that if the Hausdorff dimension of $E\subset {\mathbb{R}}^d$, $d\ge 3$, is greater than $\min \left\{\frac{dk+1}{k+1},\frac{d+k}{2}\right\},$ then the $\left(\genfrac{}{}{0ex}{}{k+1}{2}\right)$-d…