We obtain an improved Fourier restriction estimate for a truncated cone using the method of polynomial partitioning in dimension , which in particular solves the cone restriction conjecture for , and recovers the sharp range for . The main ingredient of the proof is a -broad estimate for the cone extension operator, which is a weak version of the -linear cone restriction conjecture for .
Cite this article
Yumeng Ou, Hong Wang, A cone restriction estimate using polynomial partitioning. J. Eur. Math. Soc. 24 (2022), no. 10, pp. 3557–3595DOI 10.4171/JEMS/1168