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arXiv · 2411.04438

A Kakeya maximal estimate for regulus strips

Shukun Wu
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Abstract

We prove Kakeya-type estimates for regulus strips. As a result, we obtain another epsilon improvement over the Kakeya conjecture in $\mathbb{R}^3$, by showing that the regulus strips in the ${\rm SL}_2$ example are essentially disjoint. We also establish an $L^p$ inequality regarding Nikodym-type maximal function in the first Heisenberg group.

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Shukun Wu. 2024-11-07. A Kakeya maximal estimate for regulus strips. https://arxiv.org/abs/2411.04438

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