A cone restriction estimate using polynomial partitioning

2017/04/18 by Ou, Yumeng, Wang, Hong · 1 citation
#42B10 #42B20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1704.05485

Abstract

We obtain improved Fourier restriction estimate for the 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 estimate for 2≤ k≤ n.

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