Restriction estimates for 2D surfaces of finite type 3 and applications to dispersive equations

Abstract

In this paper, we prove the restriction estimates for 2D surfaces S:= {(xi1, xi2, xi1^3 +/- xi2^3) : (xi1, xi2) in [0,1]^2} by reducing to Wang-Wu's result on the perturbed paraboloid and to the results on the perturbed hyperboloid obtained by Buschenhenke, M\"uller, and Vargas, as well as by Guo and Oh. The method is based on the rescaling technique developed in [LMZ21]. Besides, we will use the estimates to give a better analysis for discrete nonlinear Schr\"odinger equations.