Existence of conformal metrics with constant scalar curvature and constant boundary mean curvature on compact manifolds

We study the problem of deforming a Riemannian metric to a conformal one with nonzero constant scalar curvature and nonzero constant boundary mean curvature on a compact manifold of dimension n >= 3. We prove the existence of such conformal metrics in the cases of n = 6, 7 or the manifold is spin and some other remaining ones left by Escobar. Furthermore, in the positive Yamabe constant case, by normalizing the scalar curvature to be 1, there exists a sequence of conformal metrics such that their constant boundary mean curvatures go to +infinity.