Best Stein–Tomas conjecture for quadratic manifolds

Let $\mathbf{Q}$ be a quadratic manifold, and let “well-curved” and “best Stein–Tomas” denote the geometric and Fourier-analytic conditions defined in the paper. Best Stein–Tomas conjecture. $\mathbf{Q}$ satisfies the best Stein–Tomas condition if and only if it is well-curved. This would clarify whether well-curvedness implies the best Stein–Tomas condition; the paper states that no counterexample is known, but does not provide a complete answer.