Slicing surfaces and Fourier restriction conjecture
Abstract
Description
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.
13 pages, Proceedings of the Edinburgh Mathematical Society, to appear
13 pages, Proceedings of the Edinburgh Mathematical Society, to appear