CONFORMAL DEFORMATION OF A RIEMANNIAN METRIC TO A CONSTANT SCALAR CURVATURE METRIC WITH CONSTANT MEAN-CURVATURE ON THE BOUNDARY

Let (M-n,g) be a compact Riemannian manifold with boundary and n great er than or equal to 3. We show that for almost any (M-n,g) there exist s a metric within the conformal class of g having constant scalar curv ature on M and constant mean curvature on the boundary. The problem is equivalent to finding a positive solution to a semilinear elliptic eq uation with a non-linear boundary condition with critical Sobolev expo nents in the interior and on the boundary.