 This is a sort of converse question to the embedding theorems discussed above.In this direction Jeffrey Case, Sagun Chanillo and Paul C. Yang have proved a stability theorem.That is, if one starts with a family of compact CR manifolds embedded in formula_50 and the CR structure of the family formula_51 changes in a real-analytic way with respect to the parameter formula_52 and the CR Yamabe constant of the family of manifolds is uniformly bounded below by a positive constant, then the CR Paneitz operator remains non-negative for the entire family, provided one member of the family has its CR Paneitz operator non-negative.