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Bilinear restriction estimates for surfaces with curvatures of different signs

Author(s): Sanghyuk Lee
Journal: Trans. Amer. Math. Soc. 358 (2006), 3511-3533.
MSC (2000): Primary 42B15
Posted: August 1, 2005
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Abstract: Recently, the sharp $L^2$-bilinear (adjoint) restriction estimates for the cone and the paraboloid were established by Wolff and Tao, respectively. Their results rely on the fact that for the cone and the paraboloid, the nonzero principal curvatures have the same sign. We generalize those bilinear restriction estimates to surfaces with curvatures of different signs.

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Additional Information:

Sanghyuk Lee
Affiliation: Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, Korea
Address at time of publication: Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706-1388
Email: sanghyuk@postech.ac.kr, slee@math.wisc.edu

DOI: 10.1090/S0002-9947-05-03796-7
PII: S 0002-9947(05)03796-7
Keywords: Fourier transform, restriction estimates
Received by editor(s): January 12, 2004
Received by editor(s) in revised form: June 24, 2004
Posted: August 1, 2005
Additional Notes: Research of the author was supported in part by The Interdisciplinary Research Program R01-1999-00005 (primary investigator: K.-T. Kim) of The Korea Science and Engineering Foundation.
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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