Abstract: We consider the global embedding problem for compact, three dimensional
CR manifolds. Sufficient conditions for embeddability are obtained from assumptions on the CR Yamabe
invariant and the non-negativity of a certain conformally invariant fourth order operator called the CR Paneitz
operator. The conditions are shown to be necessary for small deformations of the standard CR structure on the three sphere.

This is a joint work with Hung-Lin Chiu and Paul Yang.