Scalar Curvature Splittings II: Removal of Singularities

Abstract

In Part I of this paper we have seen that any singular compact area minimizer in a positive scalar curvature manifold admits a conformal deformation to some minimal factor geometry that shares many properties with the minimizer, like the Ahlfors regularity, the validity of Poincare inequalities and the presence of tangent cones with positive scalar curvature. In this Part II we show that these geometries admit surgery style arguments eliminating the singular sets.