The endpoint case of the Bennett-Carbery-Tao multilinear Kakeya conjecture

TL;DR

This paper proves the endpoint case of the n-linear Kakeya conjecture in R^n, completing the proof of the conjecture formulated by Bennett, Carbery, and Tao.

Contribution

It provides a proof for the previously unresolved endpoint case of the Bennett-Carbery-Tao multilinear Kakeya conjecture.

Findings

Proved the endpoint case of the n-linear Kakeya conjecture.

Confirmed the conjecture for all cases in R^n.

Advances understanding of multilinear geometric measure theory.

Abstract

Bennett, Carbery, and Tao formulated an n-linear analogue of the Kakeya conjecture in R^n. They proved the conjecture except for the endpoint case. We prove the endpoint case.