Improved bounds for the Kakeya maximal conjecture in higher dimensions

Jonathan Hickman, Keith M. Rogers, Ruixiang Zhang

Research output: Working paper

Abstract

We adapt Guth's polynomial partitioning argument for the Fourier restriction problem to the context of the Kakeya problem. By writing out the induction argument as a recursive algorithm, additional multiscale geometric information is made available. To take advantage of this, we prove that direction-separated tubes satisfy a multiscale version of the polynomial Wolff axioms. Altogether, this yields improved bounds for the Kakeya maximal conjecture in Rn with n=5 or n≥7 and improved bounds for the Kakeya set conjecture for an infinite sequence of dimensions.
Original languageEnglish
PublisherArXiv
Number of pages43
Publication statusPublished - 14 Aug 2019

Fingerprint

Dive into the research topics of 'Improved bounds for the Kakeya maximal conjecture in higher dimensions'. Together they form a unique fingerprint.

Cite this