Bilinear restriction estimates for surfaces of codimension bigger than one

Abstract

In connection with the restriction problem in Rn for hypersurfaces including the sphere and paraboloid, the bilinear (adjoint) restriction estimates have been extensively studied. However, not much is known about such estimates for surfaces with codimension (and dimension) larger than 1. In this paper we show sharp bilinear L2L2 !Lq restriction estimates for general surfaces of higher codimension. In some special cases, we can apply these results to obtain the corresponding linear estimates.