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Let (M,g) a compact Riemannian n-dimensional manifold with umbilic boundary.It is well know that, under certain hypothesis, in the conformal class of gthere are scalar-flat metrics that have the boundary of M as a constant meancurvature hypersurface. In this paper we prove that these metrics are a compactset, provided n=8 and the Weyl tensor of the boundary is always different fromzero, or if n>8 and the Weyl tensor of M is always different from zero on theboundary.

A compactness result for scalar-flat metrics on manifolds with umbilic boundary