Slicing surfaces and Fourier restriction conjecture

Details Slicing surfaces and Fourier restriction conjecture Slicing surfaces and Fourier restriction conjecture

2008-04-23

arxiv.org/abs/0804.3696v1

Mathematics

Classical Analysis and ODEs

13 pages, Proceedings of the Edinburgh Mathematical Society, to appear

Scientific paper

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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