Let (M,g) a compact Riemannian n-dimensional manifold with umbilic boundary. It is well known 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.
Compactness for conformal scalar-flat metrics on umbilic boundary manifolds
Ghimenti M.
;Micheletti A. M.
2020-01-01
Abstract
Let (M,g) a compact Riemannian n-dimensional manifold with umbilic boundary. It is well known 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.File in questo prodotto:
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