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On a question of Bourgain about geometric incidences

Jozsef Solymosi·Csaba D. Toth
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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 $s=Ω(n^{11/4})$. This is the first nontrivial answer to a question recently posed by Jean Bourgain.

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Jozsef Solymosi, Csaba D. Toth. 2007-01-14. On a question of Bourgain about geometric incidences. https://doi.org/10.1017/s0963548308009127

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