Restriction for flat surfaces of revolution in ${\mathbf R}^3$

Anthony Carbery, Carlos E. Kenig, Sarah Ziesler

Type: Article

Publication Date: 2007-01-09

Citations: 14

DOI: https://doi.org/10.1090/s0002-9939-07-08689-3

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.

Locations

Proceedings of the American Mathematical Society - View - PDF

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