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

Abstract

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 g there are scalar-flat metrics that have the boundary of M as a constant mean curvature hypersurface. In this paper we prove that these metrics are a compact set, provided n=8 and the Weyl tensor of the boundary is always different from zero, or if n>8 and the Weyl tensor of M is always different from zero on the boundary.

References in corpus (4)

• Barycenter technique and the Riemann mapping problem of Escobar
• A compactness theorem for scalar-flat metrics on manifolds with boundary
• Blow-up phenomena for scalar-flat metrics on manifolds with boundary
• Conformal Deformation to Scalar Flat Metrics with Constant Mean Curvature on the Boundary in Higher Dimensions

Cited by in corpus (1)

• Compactness of scalar-flat conformal metrics on low-dimensional manifolds with constant mean curvature on boundary