Attaching faces of positive scalar curvature manifolds with corners

Abstract

We prove a novel desingularization theorem, that allows to smoothly attach two given manifolds with corners by suitably gluing a pair of isometric faces, with control on both the scalar curvature of the resulting space and the mean curvature of its boundary.

final preprint version, to appear in Beijing Journal of Pure and Applied Mathematics (invited contribution for the Bartnik memorial volume)