Geometric & Functional Analysis GAFA

, Volume 13, Issue 6, pp 1359–1384

A sharp bilinear restriction estimate for paraboloids

Original Article

DOI: 10.1007/s00039-003-0449-0

Cite this article as:
Tao, T. Geom. funct. anal. (2003) 13: 1359. doi:10.1007/s00039-003-0449-0

Abstract

Recently Wolff [W3] obtained a sharp L2 bilinear restriction theorem for bounded subsets of the cone in general dimension. Here we adapt the argument of Wolff to also handle subsets of “elliptic surfaces” such as paraboloids. Except for an endpoint, this answers a conjecture of Machedon and Klainerman, and also improves upon the known restriction theory for the paraboloid and sphere.

Keywords.

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Mathematics Subject Classification (2000).

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Copyright information

© Birkhäuser-Verlag 2003

Authors and Affiliations

  1. 1.Department of MathematicsUCLALos AngelesUSA

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