Bilinear restriction estimates for surfaces with curvatures of different signs
By Sanghyuk Lee. 2005
79 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/9f64d7abc7ba4027f29723abed3c104a2c1a0d8f
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In Applied Mathematics
- Keith McKenzie Rogers
- Jonathan Bennett
- Sanghyuk Lee
- Larry Guth
- Xiumin Du
- Jean Bourgain
- Renato Lucà
- Ruixiang Zhang
In Mathematical Physics
- Keith McKenzie Rogers
- Jonathan Bennett
- Sanghyuk Lee
- Larry Guth
- Jean Bourgain
- Xiumin Du
- Renato Lucà
- J. Hickman
Citations in the corpus
- Aspects of Multilinear Harmonic Analysis Related to Transversality (2014, background): “4This conjecture is known to be false for surfaces with nonvanishing curvatures of different sign, such as the saddle; see [35] and [53].”
- Linear and bilinear estimates for oscillatory integral operators related to restriction to hypersurfaces (2006, methodology): “It also contains the results for the conic surfaces with curvatures of different signs in [10].”
- A local smoothing estimate for the Schrödinger equation (2008, methodology): “In two spatial dimensions, by a restriction theorem independently due to Vargas [34] and Lee [18], we have the result in the range q 10/3.”
- Improved bounds for Stein's square functions (2010, unknown): “Tao’s bilinear adjoint restriction theorem [23, 41].”