Bilinear restriction estimates for surfaces with curvatures of different signs
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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.References
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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
- Received by editor(s): January 12, 2004
- Received by editor(s) in revised form: June 24, 2004
- Published electronically: 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 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 358 (2006), 3511-3533
- MSC (2000): Primary 42B15
- DOI: https://doi.org/10.1090/S0002-9947-05-03796-7
- MathSciNet review: 2218987