A compactness theorem for scalar-flat metrics on 3-manifolds with boundary
arXiv:1807.08406 · doi:10.1016/j.jfa.2019.01.001
Abstract
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.
Final version, to appear in the Journal of Functional Analysis. arXiv admin note: text overlap with arXiv:0906.0927