The Kakeya conjecture on local fields of positive characteristic

TL;DR

This paper proves an analogue of the Kakeya conjecture and the Kakeya maximal conjecture for local fields of positive characteristic, extending previous results to a new setting.

Contribution

It extends Arsovski's results by establishing the Kakeya and Kakeya maximal conjectures for local fields of positive characteristic.

Findings

Proved the Kakeya conjecture analogue for $ ext{F}_q( ext{(t)})$

Established the Kakeya maximal conjecture in this setting

Extended previous results to local fields of positive characteristic

Abstract

We state and prove an analogue of the Kakeya conjecture for the local field $\mathbb{F}_q(\!(t)\!)$. This extends Arsovski's result on the Kakeya conjecture to local fields of positive characteristic. We also prove the Kakeya maximal conjecture in this setting.