Equivalence of linear and trilinear Kakeya conjectures in three dimensions

TL;DR

This paper establishes that two major Kakeya conjectures in three dimensions, the Kakeya maximal operator conjecture and its trilinear dual form, are mathematically equivalent, linking different approaches to understanding Kakeya sets.

Contribution

It proves the equivalence between the Kakeya maximal operator conjecture and its disjoint trilinear dual form in three dimensions, unifying two key conjectures.

Findings

Proves the equivalence of the two Kakeya conjectures in three dimensions

Links the maximal operator conjecture with its trilinear dual form

Provides a unified framework for Kakeya conjecture approaches

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