A bound for plany Kakeya sets in ${\mathbb{F}}_q^4$ using the planebrush method

Abstract

Katz and Zahl used a planebrush argument to prove that Kakeya sets in ${\mathbb{R}}^4$ have Hausdorff dimension at least 3.059. In the special case when the Kakeya set is plany, their argument gives a better lower bound of 10/3. We give a nontechnical exposition of the Katz-Zahl argument for plany Kakeya sets in the finite field setting.

15 pages, 4 figures