Scale-invariant Fourier restriction to a hyperbolic surface

Abstract

This result sharpens the bilinear-to-linear deduction of Lee and Vargas for extension estimates on the hyperbolic paraboloid in ${ℝ}^3$ to the sharp line, leading to the first scale-invariant restriction estimates, beyond the Stein–Tomas range, for a hypersurface on which the principal curvatures have different signs.