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Sharpness Results and Knapp's Homogeneity Argument |
Canad. Math. Bull. 43(2000), 63-68
Published:2000-03-01
Printed: Mar 2000
Printed: Mar 2000
- Alex Iosevich
- Guozhen Lu
Abstract
We prove that the $L^2$ restriction theorem, and $L^p \to L^{p'}$,
$\frac{1}{p}+\frac{1}{p'}=1$, boundedness of the surface averages
imply certain geometric restrictions on the underlying
hypersurface. We deduce that these bounds imply that a certain
number of principal curvatures do not vanish.
| MSC Classifications: | 42B99 - None of the above, but in this section |