Restriction for flat surfaces of revolution in 𝐑³

Carbery, A.; Kenig, C.; Ziesler, S.

doi:10.1090/S0002-9939-07-08689-3

Restriction for flat surfaces of revolution in ${\mathbf R}^3$
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by A. Carbery, C. Kenig and S. Ziesler PDF

Proc. Amer. Math. Soc. 135 (2007), 1905-1914 Request permission

Abstract:

We investigate restriction theorems for hypersurfaces of revolution in $\mathbf {R}^3,$ with affine curvature introduced as a mitigating factor. Abi-Khuzam and Shayya recently showed that a Stein-Tomas restriction theorem can be obtained for a class of convex hypersurfaces that includes the surfaces $\Gamma (x)=(x,e^{-1/|x|^m}), m\geq 1.$ We enlarge their class of hypersurfaces and give a much simplified proof of their result.

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