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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: A. Carbery, C. Kenig and S. Ziesler
Journal: Proc. Amer. Math. Soc. 135 (2007), 1905-1914
MSC (2000): Primary 42B99
Published electronically: January 9, 2007
MathSciNet review: 2286103
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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/\vert x\vert^m}), m\geq 1.$ We enlarge their class of hypersurfaces and give a much simplified proof of their result.


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Additional Information

A. Carbery
Affiliation: Department of Mathematics, University of Edinburgh, Edinburgh EH9 2BJ, United Kingdom
Email: a.carbery@ed.ac.uk

C. Kenig
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Email: cek@math.uchicago.edu

S. Ziesler
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Email: ziesler@math.uchicago.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08689-3
PII: S 0002-9939(07)08689-3
Received by editor(s): December 7, 2005
Received by editor(s) in revised form: February 27, 2006
Published electronically: January 9, 2007
Additional Notes: The first author was supported in part by a Leverhulme Study Abroad Fellowship
The second author was supported in part by an NSF grant
Communicated by: Andreas Seeger
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.