Adapted complex tubes on the symplectization of pseudo-Hermitian manifolds (Q623430)

Let \((M,\theta)\) be a smooth pseudo-Hermitian manifold of real odd dimension and consider \((U,J)\) an adapted complex tube over \((M,\theta)\). The authors construct a canonical defining function for \(M\) inside the tube which satisfies the homogeneous complex Monge-Ampère equation. If \((M,\theta)\) are real analytic then they show that there is a unique maximal adapted complex tube.