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.

arXiv comment24 pages, 0 figures. This article builds upon arXiv:1807.10940

References in corpus (6)

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• Polynomial Wolff axioms and Kakeya-type estimates in ${\mathbb{R}}^4$
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Cited by in corpus (4)

• New Kakeya estimates using Gromov's algebraic lemma
• New bounds for Stein's square functions in higher dimensions
• Restriction estimates for one class of hypersurfaces with vanishing curvature in ${\mathbb{R}}^n$
• A new approach to the Fourier extension problem for the paraboloid