Convergence of scalar-flat metrics on manifolds with boundary under a   Yamabe-type flow
  We study a conformal flow for compact Riemannian manifolds of dimension greater than two with boundary. Convergence to a scalar-flat metric with constant mean curvature on the boundary is established in dimensions up to seven, and in any dimensions if the manifold is spin or if it satisfies a generic condition. 
Sergio Almaraz
math.DG math.AP