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Abstract 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… Click to show full abstract
Abstract 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 for $k\in\{2,\dots,n+1\}$ forming a $(k-1)$ -simplex.
Journal Title: Glasgow Mathematical Journal
Year Published: 2020
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