Global restriction estimates for elliptic hyperboloids

Abstract

We prove global Fourier restriction estimates for elliptic, or two-sheeted, hyperboloids of arbitrary dimension $d\ge 2$, extending recent joint work with Oliveira e Silva and Stovall. Our results are unconditional in the (adjoint) bilinear range, $q>\frac{2(d+3)}{d+1}$, and extend conditionally upon further progress toward the local restriction conjecture for elliptic surfaces.