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October 2, 2025Open Access

A bound for plany Kakeya sets in Fq⁴ using the planebrush method

Key Points

Plany kakeya sets in finite fields are shown to have a hausdorff dimension of at least 10/3.
Katz and Zahl's method provides insights into the structure and properties of kakeya sets.
The planebrush method offers a novel approach to examining dimensionality in finite field contexts.
This exposition aims to clarify the intricacies of the kakeya problem while accommodating a non-technical audience.

Abstract

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. (Sun,) studied this question.

www.synapsesocial.com/papers/68de5da283cbc991d0a20976 — DOI: https://doi.org/10.48550/arxiv.2507.09605

Authors

Izabella Łaba

Mukul Choudhuri

Joshua Zahl

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A bound for plany Kakeya sets in Fq⁴ using the planebrush method

Key Points

Abstract

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Cite this study

Authors

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