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A Kakeya maximal estimate for regulus strips

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arxiv 2411.04438 v2 pith:ASRRJSKY submitted 2024-11-07 math.CA

Shukun Wu This is my paper · ORCID
classification math.CA
keywords regulusstripskakeyamaximalanotherconjecturedisjointepsilon
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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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  1. Restriction estimates using decoupling theorems and two-ends Furstenberg inequalities

    math.CA 2024-11 conditional novelty 8.0 of 10

    The authors prove the restriction conjecture for p > 22/7 in R^3 and new higher-dimensional bounds by combining decoupling theorems with new two-ends Furstenberg incidence estimates.

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