A bound for plany Kakeya sets in $\mathbb{F}_q^4$ using the planebrush method
Classical Analysis and ODEs
2026-01-13 v1 Combinatorics
Abstract
Katz and Zahl used a planebrush argument to prove that Kakeya sets in 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.
Cite
@article{arxiv.2507.09605,
title = {A bound for plany Kakeya sets in $\mathbb{F}_q^4$ using the planebrush method},
author = {Izabella Łaba and Mukul Rai Choudhuri and Joshua Zahl},
journal= {arXiv preprint arXiv:2507.09605},
year = {2026}
}
Comments
15 pages, 4 figures