A compactness theorem for scalar-flat metrics on 3-manifolds with boundary

摘要

Let (M, g) be a compact Riemannian three-dimensional manifold with boundary. We prove the compactness of the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface. This involves a blow-up analysis of a Yamabe-type equation with critical Sobolev exponent on the boundary. (C) 2019 Elsevier Inc. All rights reserved.