Hickman, Jonathan; Rogers, Keith M. Improved Fourier restriction estimates in higher dimensions. (English) Zbl 1423.42011 Camb. J. Math. 7, No. 3, 219-282 (2019). Guth’s approach to the Fourier restriction problem via polynomial partitioning is a basic tool. Improved bounds for the restriction conjecture, particularly in high dimensions, are then obtained by writing out Guth’s induction argument as a recursive algorithm and introducing new geometric information, known as the polynomial Wolff axioms. Consequences for the Kakeya conjecture are also considered. Reviewer: Elijah Liflyand (Ramat-Gan) Cited in 20 Documents MSC: 42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.) Keywords:Fourier transform; polynomial partitioning; restriction PDFBibTeX XMLCite \textit{J. Hickman} and \textit{K. M. Rogers}, Camb. J. Math. 7, No. 3, 219--282 (2019; Zbl 1423.42011) Full Text: DOI arXiv