Preprint A271/2004
Existence results for the Yamabe problem on manifolds with boundary
Fernando C Marques
Given a compact Riemannian manifold with umbilic boundary, we prove existence of conformally related metrics of zero scalar curvature and constant mean curvature on the boundary, under hypotheses on the Weyl tensor. In order to carry out the estimates on the Sobolev quotient, we also prove existence of conformal Fermi coordinates.