A compactness theorem for conformal metrics with constant scalar curvature and constant boundary mean curvature in dimension three

Abstract

On a compact three-dimensional Riemannian manifold with boundary, we prove the compactness of the full set of conformal metrics with positive constant scalar curvature and constant mean curvature on the boundary. This involves a blow-up analysis of a Yamabe equation with critical Sobolev exponents both in the interior and on the boundary.

In this new version, we slightly rephrase the statements of Theorems 1.1 and 1.2 to reflect the dependence on the constant c. arXiv admin note: text overlap with arXiv:1807.08406