On distinct distances in homogeneous sets in the Euclidean space

J. Solymosi, Cs. D. Toth

A homogeneous set of $n$ points in the $d$-dimensional Euclidean space determines at least $\Omega (n^{2d/(d^2+1)}/{\log }^{c(d)}n)$ distinct distances for a constant $c(d)>0$. In three-…