Dimension of Pinned Distance Sets for Semi-Regular Sets

Jacob B. Fiedler, D. M. Stull

We prove that if $E\subseteq {\mathbb{R}}^2$ is analytic and $1<d<{\dim }_H(E)$, there are ``many'' points $x\in E$ such that the Hausdorff dimension of the pinned distance set ${\Delta }_{x}E$ is at…