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arXiv · 2610.12480

New bound on the Hausdorff dimension of Kakeya sets in $\mathbb{R}^4$

Mukul Rai Choudhuri
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Abstract

We obtain a slight improvement to the trilinear bound of Guth-Zahl by application of Wang-Zahl's resolution of 3-D Kakeya to tubes inside a thickened neighborhood of a variety. This is combined with the planebrush argument of Katz and Zahl to obtain the new bound of 3.073.

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Mukul Rai Choudhuri. 2026-08-30. New bound on the Hausdorff dimension of Kakeya sets in $\mathbb{R}^4$. https://arxiv.org/abs/2610.12480

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