On the distance sets of AD-regular sets

Tuomas Orponen

Published 2015-09-22Version 1

I prove that if $K \subset \mathbb{R}^{2}$ is $s$-Ahlfors-David regular with $s \geq 1$, then $$\overline{\dim}_{\mathrm{B}} D(K) = 1,$$ where $D(K) = \{|x - y| : x,y \in K\}$ is the distance set of $K$.