Analysis reveals that plany kakeya sets in finite fields have a hausdorff dimension of 10/3, highlighting important properties.
Katz and Zahl used a planebrush argument to prove that Kakeya sets in R⁴ 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.
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Łaba et al. (2025) studied this question.
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