The optimal trilinear restriction estimate for a class of hypersurfaces with curvature

In [4] nearly optimal L1 trilinear restriction estimates in Rn+1 are established under transversality assumptions only. In this paper we show that the curvature improves the range of exponents, by establishing Lp estimates, for any p>2(n+4)3(n+2) in the case of double-conic surfaces. The exponent 2(n+4)3(n+2) is shown to be the universal threshold for the trilinear estimate.