A cone restriction estimate using polynomial partitioning

Abstract

We obtain an improved Fourier restriction estimate for a truncated cone using the method of polynomial partitioning in dimension n ≥3, which in particular solves the cone restriction conjecture for n = 5, and recovers the sharp range for 3 ≤ n ≤ 4. The main ingredient of the proof is a k-broad estimate for the cone extension operator, which is a weak version of the k-linear cone restriction conjecture for 2 ≤ k ≤ n.