Résume | The study of positive scalar curvature on noncompact manifolds has seen significant progress in the last few years. Having the classic work of Schoen-Yau in mind, we describe two recent contributions: a generalization of classic obstructions to positive scalar curvature to the setting of noncompact spaces, and a new positive mass theorem that allows for incomplete spaces and, in a quantitative sense, regions of negative scalar curvature. Both are joint with R.Unger and S-T. Yau. |