Improved Fourier restriction estimates in higher dimensions

Abstract

We consider Guth's approach to the Fourier restriction problem via polynomial partitioning. By writing out his induction argument as a recursive algorithm and introducing new geometric information, known as the polynomial Wolff axioms, we obtain improved bounds for the restriction conjecture, particularly in high dimensions. Consequences for the Kakeya conjecture are also considered.

43 pages, 5 figures. A number of typos have been corrected and additional points of clarification added. To appear in Cambridge Journal of Mathematics