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A sharp bilinear restriction estimate for paraboloids

Terence Tao
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Abstract

Recently Wolff obtained a sharp $L^2$ 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 and spheres. 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.

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Terence Tao. 2002-12-13. A sharp bilinear restriction estimate for paraboloids. https://arxiv.org/abs/math/0210084

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