A refined trilinear Kakeya estimate in ℝ³

2025/06/23 by Ramos, Javier
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.18769

Abstract

We prove a refined trilinear Kakeya estimate in three dimensions, valid for small values of the transversality parameter.

Citations

• Spectral Dimension Flow, Localized Non-Orientable Horizon Defects, and Emergent Time in Black Holes: A Geometry-Driven Effective Framework
• On almost everywhere convergence of planar Bochner-Riesz means
• Sticky Kakeya sets and the sticky Kakeya conjecture
• Improved bounds for the Kakeya maximal conjecture in higher dimensions
• The trilinear restriction estimate with sharp dependence on the transversality
• The proof of the l² Decoupling Conjecture
• The endpoint multilinear Kakeya theorem via the Borsuk--Ulam theorem
• Bounds on oscillatory integral operators based on multilinear estimates
• The endpoint case of the Bennett-Carbery-Tao multilinear Kakeya conjecture
• On the Multilinear Restriction and Kakeya conjectures
• On the multilinear restriction and Kakeya conjectures
• On a planar variant of the Kakeya problem
• A bilinear approach to the restriction and Kakeya conjectures

Related

• The trilinear restriction estimate with sharp dependence on the transversality
• A comparison of trilinear testing conditions for the paraboloid Fourier extension and Kakeya conjectures in three dimensions
• Equivalence of linear and trilinear Kakeya conjectures in three dimensions
• Introduction to the proof of the Kakeya conjecture
• New curved Kakeya estimates