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October 9, 20250 citationsOpen Access

Equivalence of linear and trilinear Kakeya conjectures in three dimensions

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CRCristian RiosESEric T. Sawyer

Key Points

  • 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.

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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Cite This Study

Rios et al. (2025) studied this question.

synapsesocial.com/papers/68e8439a9989581a2fd4e23chttps://doi.org/10.48550/arxiv.2506.21315
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1On Kakeya’s maximal function II: high dimensional cases2024
  2. 2Dimensional Invariance in Zero-Measure Spaces: An N-Dimensional Algebraic Generalization of the Kakeya Conjecture via Seonggil Field Equations2026
  3. 3Proof of the High-Dimensional Kakeya Maximal Conjecture (n ≥ 4) Based on the UTE General Transport Equation Framework2026
  4. 4A Proof of the Kakeya Conjecture via High-Dimensional Symmetric Topology and Measure Shrinkage2026
  5. 5The D-equivalence conjecture for hyper-K\"ahler varieties via hyperholomorphic bundles2024