A compactness result for scalar-flat metrics on low dimensional manifolds with umbilic boundary
Differential Geometry
2020-09-03 v1 Analysis of PDEs
Abstract
Let (M,g) a compact Riemannian -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 in the case of low dimensional manifolds, that is n=6,7,8, provided that the Weyl tensor is always not vanishing on the boundary.
Keywords
Cite
@article{arxiv.2009.00989,
title = {A compactness result for scalar-flat metrics on low dimensional manifolds with umbilic boundary},
author = {Marco G. Ghimenti and Anna Maria Micheletti},
journal= {arXiv preprint arXiv:2009.00989},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1903.10990, arXiv:1912.11482