Falconer distance problem on Riemannian manifolds

Changbiao Jian, Bochen Liu, Yakun Xi

We prove that on a $d$-dimensional Riemannian manifold, the distance set of a Borel set $E$ has a positive Lebesgue measure if $$\dim_{\mathcal{H}}(E)>\frac d2+\frac14+\frac{1-(-1)…