Terence Tao
Published 2002-10-07, updated 2002-12-13Version 2
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.
Comments: 21 pages, no figures, to appear, GAFA. More explanation added and some minor typos removed
An improved bilinear restriction estimate for paraboloid in $\mathbb{R}^3$
A distinction between the paraboloid and the sphere in weighted restriction
Small cap decoupling for paraboloid in $\mathbb{R}^n$
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