Pinned geometric configurations in Euclidean space and Riemannian manifolds

Alex Iosevich, Krystal Taylor, Ignacio Uriarte-Tuero

Let $M$ be a compact $d$-dimensional Riemannian manifold without a boundary. Given $E\subset M$, let ${\Delta }_{\rho }(E)=\{\rho (x,y):x,y\in E\}$, where $\rho$ is the Riemannian metric on $M$. Le…