Existence results for the Yamabe problem on manifolds with boundary Fernando Marques 53C2558J60Yamabe problemscalar curvaturemean curvatureWeyl tensor Given a compact Riemannian manifold with umbilic boundary, we prove the existence of conformally related metrics of zero scalar curvature and constant mean curvature on the boundary, under suitable hypotheses on the Weyl tensor. In order to carry out the estimates on the Sobolev quotient, we also prove the existence of conformal Fermi coordinates. Indiana University Mathematics Journal 2005 text pdf 10.1512/iumj.2005.54.2590 10.1512/iumj.2005.54.2590 en Indiana Univ. Math. J. 54 (2005) 1599 - 1620 state-of-the-art mathematics http://iumj.org/access/