A cone restriction estimate using polynomial partitioning (Q2148896)

Summary: 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 \(2\leq k\leq n\).