We show that an orientable –dimensional manifold admits a complete riemannian metric of bounded geometry and uniformly positive scalar curvature if and only if there exists a finite collection of spherical space-forms such that is a (possibly infinite) connected sum where each summand is diffeomorphic to or to some member of . This result generalises G Perelman’s classification theorem for compact –manifolds of positive scalar curvature. The main tool is a variant of Perelman’s surgery construction for Ricci flow.
"Ricci flow on open $3$–manifolds and positive scalar curvature." Geom. Topol. 15 (2) 927 - 975, 2011. https://doi.org/10.2140/gt.2011.15.927