Equivalence of linear and trilinear Kakeya conjectures in three dimensions

2025/06/26 by Cristian Rios, Eric T. Sawyer, Rios, Cristian +1
Economics, Econometrics and Finance · Mathematics · Decision Sciences · #Housing Market and Economics #Advanced Harmonic Analysis Research #Probability and Risk Models

paper · pdf · doi:10.48550/arxiv.2506.21315

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

Citations

• Trilinear characterizations of the Fourier extension conjecture on the paraboloid in three dimensions
• Bounds on oscillatory integral operators based on multilinear estimates
• On the Multilinear Restriction and Kakeya conjectures
• On the multilinear restriction and Kakeya conjectures
• A bilinear approach to the restriction and Kakeya conjectures

Cited by

• Trilinear characterizations of the Fourier extension conjecture on the paraboloid in three dimensions

Related

• Introduction to the proof of the Kakeya conjecture
• A refined trilinear Kakeya estimate in ℝ³
• A Survey of the Kakeya Conjecture, 2000–2025
• New bounds on Kakeya problems
• A comparison of trilinear testing conditions for the paraboloid Fourier extension and Kakeya conjectures in three dimensions