Nonempty interior of pinned distance and tree sets

Tainara Borges, Benjamin Foster, Yumeng Ou +1

For a compact set $E\subset {\mathbb{R}}^d$, $d\ge 2$, consider the pinned distance set ${\Delta }^y(E)=\{|x-y|:x\in E\}$. Peres and Schlag showed that if the Hausdorff dimens…