A cone restriction estimate using polynomial partitioning

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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 .