Endpoint bounds for the non-isotropic Falconer distance problem associated with lattice-like sets

A. Iosevich, M. Rudnev

Let $S\subset {\mathbb{R}}^d$ be contained in the unit ball. Let $\Delta (S)=\{||a-b||:a,b\in S\}$, the Euclidean distance set of $S$. Falconer conjectured that the $\Delta (S)$ has positive…