A compactness result for the CR Yamabe problem in three dimensions

We prove the compactness of the set of solutions to the CR Yamabe problem on a compact strictly pseudoconvex CR manifold of dimension three whose blow-up manifolds at every point have positive p-mass. As a corollary, we deduce that compactness holds for CR-embeddable manifolds which are not CR-equivalent to $S^3$. The theorem is proved by blow-up analysis.