  We solve the remaining cases of the Riemann mapping problem of Escobar.
Indeed, performing a suitable scheme of the barycenter technique of Bahri-Coron
via the Chen's bubbles, we solve the cases left open after the work of Chen.
Thus, combining our work with the ones of Almaraz, Chen, Escobar and Marques we
have that every compact Riemannian manifold with boundary of dimension greater
or equal than 3 carries a conformal scalar flat metric with constant mean
curvature.
