The lock principle for scalar curvature

Abstract

We prove a Riemannian positive mass theorem for asymptotically flat spin manifolds with hypersurface singularities. Unlike earlier results, some components of the singular set may be mean-concave, provided that other components of the singular set are sufficiently mean-convex. Our proof uses initial data sets where a suitably chosen second fundamental form transfers convexity defects between different singularity components.