A cone restriction estimate using polynomial partitioning

Abstract

We obtain improved Fourier restriction estimate for the truncated cone using the method of polynomial partitioning in dimension $n\ge 3$, which in particular solves the cone restriction conjecture for $n=5$, and recovers the sharp range for $3\le n\le 4$. 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 $2\le k\le n$.

36 pages

Cited by in corpus (7)

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• Improved decay of conical averages of the Fourier transform
• Fourier Restriction to a Hyperbolic Cone
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• Refined Strichartz inequalities for the wave equation
• A new approach to the Fourier extension problem for the paraboloid