Similar point configurations via group actions

P. Bhowmik, A. Greenleaf, A. Iosevich +2

We prove that for $d\ge 2,k\ge 2$, if the Hausdorff dimension of a compact set $E\subset {\mathbb{R}}^d$ is greater than $\frac{d^2}{2d-1}$, then, for any given $r>0$, there exi…