Sharp restriction estimates for several degenerate higher co-dimensional quadratic surfaces

Fourier restriction conjecture is an important problem in harmonic analysis. Guo-Oh 17 studied the restriction estimates for quadratic surfaces of co-dimension 2 in R⁵. For one special surface (₁, ₂, ₃, ₁², ₂²+₁₃), they applied a nested induction argument to build essentially sharp restriction estimate. In this paper, we simplify their method, and extend it to a variant of the broad-narrow analysis. As applications, we will prove essentially sharp restriction estimates for some kinds of degenerate higher co-dimensional quadratic surfaces.