Title: Existence results for the Yamabe problem on manifolds with boundary

Authors: Fernando Coda Marques

Issue: Volume 54 (2005), Issue 6, 1599-1620

Abstract: 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.