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Sharpness Results and Knapp’s Homogeneity Argument

Published online by Cambridge University Press:  20 November 2018

Alex Iosevich  and
Guozhen Lu
Alex Iosevich
Affiliation:
Department of Mathematics Georgetown University Washington, DC 20057 USA, email: [email protected]
Guozhen Lu
Affiliation:
Department of Mathematics Wright State University Dayton, OH 45435 USA, email: [email protected]
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Abstract

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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.

Keywords

42B99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 43 , Issue 1 , 01 March 2000 , pp. 63 - 68
Copyright
Copyright © Canadian Mathematical Society 2000

References

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