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arXiv · 0804.3696

Slicing surfaces and Fourier restriction conjecture

Fabio Nicola
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Abstract

We deal with the restriction phenomenon for the Fourier transform. We prove that each of the restriction conjectures for the sphere, the paraboloid, the elliptic hyperboloid in $\mathbb{R}^n$ implies that for the cone in $\mathbb{R}^{n+1}$. We also prove a new restriction estimate for any surface in $\mathbb{R}^3$ locally isometric to the plane and of finite type.

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Fabio Nicola. 2008-04-23. Slicing surfaces and Fourier restriction conjecture. https://arxiv.org/abs/0804.3696

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