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arXiv · 1704.05485

A cone restriction estimate using polynomial partitioning

Yumeng Ou·Hong Wang
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Abstract

We obtain improved Fourier restriction estimate for the 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 estimate for $2\leq k\leq n$.

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Yumeng Ou, Hong Wang. 2017-04-18. A cone restriction estimate using polynomial partitioning. https://arxiv.org/abs/1704.05485

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