On Falconer's distance set conjecture
Let \(E\) be a compact subset of \(\mathbb{R}^d\) and \(\Delta(E)=\{|x-y| : x,y \in E\}\). Falconer's conjecture is that if the Hausdorff dimension of \(E\) is greater than \(d/2\), then the Lebesgue measure of \(\Delta(E)\) is positive. In this paper the author proves that this is true if \(d > 2\) and \(\dim(E) > d(d+2)/2(d+1)\).
scientific article; zbMATH DE number 5152585
scientific article