October 9, 2025Open Access

Equivalence of linear and trilinear Kakeya conjectures in three dimensions

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The proof establishes that two classes of Kakeya conjectures are equivalent.
It provides a significant link between the Kakeya maximal operator conjecture and the trilinear dual form.
This finding contributes to the understanding of Kakeya conjectures in higher-dimensional spaces.
The work is significant for mathematical analysis and potential applications in geometric measure theory.

Implication

This proof demonstrates the equivalence of the Kakeya maximal operator conjecture and its trilinear dual form.

Abstract

We prove the equivalence of two Kakeya conjectures: 1.The Kakeya maximal operator conjecture 2.The disjoint trilinear dual form of the Kakeya maximal operator conjecture

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Rios et al. (2025) studied this question.

synapsesocial.com/papers/68e8439a9989581a2fd4e23c https://doi.org/10.48550/arxiv.2506.21315

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Implication

This proof demonstrates the equivalence of the Kakeya maximal operator conjecture and its trilinear dual form.

Abstract

We prove the equivalence of two Kakeya conjectures: 1.The Kakeya maximal operator conjecture 2.The disjoint trilinear dual form of the Kakeya maximal operator conjecture

Equivalence of linear and trilinear Kakeya conjectures in three dimensions

Key Points

Implication

Abstract

Discussion

Cite This Study

Equivalence of linear and trilinear Kakeya conjectures in three dimensions

Key Points

Implication

Abstract

Discussion

Cite This Study

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