Theoretical analysis demonstrates Kakeya-type estimates for regulus strips in three dimensions, indicating an improvement over the classical Kakeya conjecture.
We prove Kakeya-type estimates for regulus strips. As a result, we obtain another epsilon improvement over the Kakeya conjecture in R³ , by showing that the regulus strips in the {SL}₂ example are essentially disjoint. We also establish an Lᵖ inequality regarding a Nikodym-type maximal function in the first Heisenberg group.
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Shukun Wu (2026) studied this question.
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