2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107775We prove that any real analytic strictly pseudoconvex CR 3-manifold is the boundary (at infinity) of a unique selfdual Einstein metric defined in a neighborhood. The proof uses a new construction of twistor space based on singular rational curves.Minor corrections. To appear in: Annales de l'Institut FourierDifferential Geometrytext