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 $n\\geq 3$, which in particular solves the cone restriction conjecture for $n=5$, and recovers the sharp range for $3\\leq n\\leq 4$. 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 $2\\leq k\\leq n$.