Eyvindur Ari Palsson

On Volumes of Simplices in Intermediate Dimensions

Abstract A variant of the Falconer distance problem asks for fixed $$k\geqslant 1$$ k ⩾ 1 and $$d\geqslant k+1$$ d ⩾ k + 1 , how large does the Hausdorff dimension of a Borel set $$E\subset \mathbb {R}^d$$ E ⊂ R d need to be to guarantee that there exist $$x_0,\ldots ,x_{k}\in E$...