Title: Optimal decay constant for complete manifolds of positive scalar curvature with quadratic decay
Abstract: We prove that if an orientable 3-manifold M admits a complete Riemannian metric whose scalar curvature is positive and has at most C-quadratic decay at infinity for some C > 2β3, then it decomposes as a (possibly infinite) connected sum of spherical manifolds and π2 Γ π1 summands. Consequently, M carries a complete Riemannian metric of uniformly positive scalar curvature. The decay constant 2β3 is sharp, as demonstrated by metrics on β2 Γ π1. This improves a result of Balacheff, Gil Moreno de Mora SardΓ , and Sabourau, and partially answers a conjecture of Gromov. The main tool is a new exhaustion result using ΞΌ-bubbles.