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.
Łaba et al. (Sun,) studied this question.
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