Scalar curvature, metric degenerations and the static vacuum Einstein equations on 3-manifolds, II

Abstract

This paper is a continuation of I, (same title), and is concerned with the existence, regularity and degeneration of metrics minimizing natural curvature functionals on the space of metrics on 3-manifolds. The functionals chosen are designed to be optimal w.r.t. the issue of geometrization of the underlying 3-manifold, in the sense of Thurston. Two of the main results are Theorems B and C, in comparison with Theorem A of I.