A note on Fourier restriction and nested Polynomial Wolff axioms

Abstract

This note records an asymptotic improvement on the known $L^p$ range for the Fourier restriction conjecture in high dimensions. This is obtained by combining Guth's polynomial partitioning method with recent geometric results regarding intersections of tubes with nested families of varieties.Comment: 24 pages, 0 figures. This article builds upon arXiv:1807.1094