Abstrakt
We show that the number of unit distances determined by n points in R-3 is O(n(3/2)), slightly improving the bound of Clarkson, Edelsbrunner, Guibas, Sharir and Welzl [5], established in 1990. The new proof uses the recently introduced polynomial partitioning technique of Guth and Katz [12].
While this paper was still in a draft stage, a similar proof of our main result was posted to the arXiv by Joshua Zahl [28].