A compactness result for scalar-flat metrics on manifolds with umbilic boundary
Analysis of PDEs
2019-03-27 v1 Differential Geometry
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.
Keywords
Cite
@article{arxiv.1903.10990,
title = {A compactness result for scalar-flat metrics on manifolds with umbilic boundary},
author = {Marco Ghimenti and Anna Maria Micheletti},
journal= {arXiv preprint arXiv:1903.10990},
year = {2019}
}