Any hypersurface in \(\mathbb {R}^{d+1}\) has a Hausdorff dimension of d. However, the Fourier dimension depends on the finer geometric properties of the hypersurface. For example, the Fourier dimension of a hyperplane is 0, and the Fourier dimension of a hypersurface with non-vanishing Gaussian curvature is d. Recently, Fraser, Harris, and Kroon showed that the Euclidean light cone in \(\mathbb {R}^{d+1}\) has a Fourier dimension of \(d-1\) , which leads one to conjecture that the Fourier dimension of a hypersurface equals the number of non-vanishing principal curvatures. We prove this conjecture for all constant rank hypersurfaces. Our method involves substantial generalizations of their strategy.
