On a question of Bourgain about geometric incidences

Abstract

Given a set of $s$ points and a set of $n^2$ lines in three-dimensional Euclidean space such that each line is incident the $n$ points but no $n$ lines are coplanar, then we have $s=\Omega (n^{11/4})$. This is the first nontrivial answer to a question recently posed by Jean Bourgain.

7 pages

References in corpus (1)

• On distinct distances in homogeneous sets in the Euclidean space

Cited by in corpus (3)

• On Lines, Joints, and Incidences in Three Dimensions
• Algebraic Methods in Discrete Analogs of the Kakeya Problem
• Incidences in Three Dimensions and Distinct Distances in the Plane