ON GILP’S GROUP-THEORETIC APPROACH TO FALCONER’S DISTANCE PROBLEM

In this paper, we follow and extend a group-theoretic method introduced by Greenleaf–Iosevich–Liu–Palsson (GILP) to study finite points configurations spanned by Borel sets in \mathbb{R}^n,n\geq 2,n\in\mathbb{N}.We remove a technical continuity condition in a GILP’s theorem in [ Revista Mat. Iberoamer 31 (2015), 799–810]. This allows us to extend the Wolff–Erdogan dimension bound for distance sets to finite points configurations with k points...