In dimension 3, a non-perturbative set of conditions that are CR invariant has been found by Sagun Chanillo, Hung-Lin Chiu and Paul C. Yang that guarantees global embeddability for abstract strongly pseudo-convex CR structures defined on compact manifolds. Under the hypothesis that the CR Paneitz Operator is non-negative and the CR Yamabe constant is positive, one has global embedding. The second condition can be weakened to a non-CR invariant condition by demanding the Webster curvature of the abstract manifold be bounded below by a positive constant. It allows the authors to get a sharp lower bound on the first positive eigenvalue of Kohn's Laplacian. The lower bound is the analog in CR Geometry of the André Lichnerowicz bound for the first positive eigenvalue of the Laplace–Beltrami operator for compact manifolds in Riemannian geometry. Non-negativity of the CR Paneitz operator in dimension 3 is a CR invariant condition as follows by the conformal covariant properties of the CR Paneitz operator on CR manifolds of real dimension 3, first observed by Kengo Hirachi. The CR version of the Paneitz operator, the so-called CR Paneitz Operator first appears in a work of C. Robin Graham and John Lee. The operator is not known to be conformally covariant in real dimension 5 and higher, but only in real dimension 3. It is always a non-negative operator in real dimension 5 and higher.