A note on Fourier restriction and nested Polynomial Wolff axioms

TL;DR

This paper presents an asymptotic improvement on the Fourier restriction conjecture in high dimensions by combining polynomial partitioning with geometric intersection results.

Contribution

It introduces a novel combination of Guth's polynomial partitioning method with recent geometric intersection results to improve the Fourier restriction range.

Findings

Improved the known $L^p$ range for Fourier restriction in high dimensions.

Combined polynomial partitioning with geometric intersection results.

Achieved an asymptotic enhancement over previous bounds.

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.