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arXiv · 2009.00989

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

Marco G. Ghimenti·Anna Maria Micheletti
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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 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.

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Marco G. Ghimenti, Anna Maria Micheletti. 2020-09-01. A compactness result for scalar-flat metrics on low dimensional manifolds with umbilic boundary. https://arxiv.org/abs/2009.00989

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