A Mattila-Sjölin theorem for triangles

Eyvindur Ari Palsson, Francisco Romero Acosta

We show for a compact set $E\subset {\mathbb{R}}^d$, $d\ge 4$, that if the Hausdorff dimension of $E$ is larger than $\frac{2}{3}d+1$, then the set of congruence classes of triang…