A sharp bilinear restriction estimate for paraboloids

Research paper by Terence Tao

Indexed on: 01 Dec '03Published on: 01 Dec '03Published in: Geometric and Functional Analysis


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.