| Abstract: |
If Γ is a C3 hypersurface in Rn and dσ is induced Lebesgue measure on Γ, then it is well known that a Tomas-Stein Fourier restriction estimate on Γ implies that Γ has a nowhere vanishing Gaussian curvature. In a recent paper, Carbery and Ziesler observed that if induced Lebesgue measure is replaced by affine surface area, then a Tomas-Stein restriction estimate on Γ implies that Γ satisfies the affine isoperimetric inequality. Since the only property needed for a hypersurface to satisfy the affine isoperimetric inequality is convexity, this raised the question of whether a TomasStein restriction estimate can be obtained for flat but convex hypersurfaces in Rn such as Γ(x) = (x, e−1/ $m ), m = 1, 2, . . . . We prove that this is indeed the case in dimension n = 3. |
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