Full Fourier spectrum for general domains

Determine the full Fourier spectrum of Gaussian multiplicative chaos restrictions to more general domains beyond the flat-boundary and uniformly strictly convex cases.

Background

The paper determines several endpoint Fourier-dimension formulas for Gaussian multiplicative chaos restricted to Euclidean domains, including finite-perimeter lower bounds, exact results for domains with flat boundary patches, and exact formulas for uniformly strictly convex domains. It also derives partial information about the Fourier spectrum, including concavity-based lower bounds and an upper bound for domains with flat open boundary patches.

The complete Fourier spectrum remains unresolved for more general domains. This problem concerns determining the spectrum across all interpolation parameters, not merely the ordinary Fourier dimension or the Sobolev endpoint.