English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we follow and extend a group-theoretic method introduced byGreenleaf-Iosevich-Liu-Palsson (GILP) to study finite points configurationsspanned by Borel sets in $\mathbb{R}^n,n\geq 2,n\in\mathbb{N}.$ We remove atechnical continuity condition in a GILP's theorem in [GILP15]. This allows usto extend the Wolff-Erdogan dimension bound for distance sets to finite pointsconfigurations with $k$ points for $k\in\{2,\dots,n+1\}.$ At the end of thispaper, we extend this group-theoretic method and illustrate a `Fourier free'approach to Falconer's distance set problem for the Lebesgue measure. Weexplain how to use tubular incidence estimates in distance set problems.Curiously, tubular incidence estimates are also related to the Kakeya problem.

On GILP's group theoretic approach to Falconer's distance problem