An Incidence Result for Well-Spaced Atoms in all Dimensions

Abstract

We prove an incidence result counting the $k$-rich $\delta$-tubes induced by a well-spaced set of $\delta$-atoms. Our result coincides with the bound that would be heuristically predicted by the Szemerédi--Trotter Theorem and holds in all dimensions $d\ge 2$.

9 pages. Comments welcome