https://arxiv.org/abs/1711.02457 Deforming 3-manifolds of bounded geometry and uniformly positive scalar curvature
Laurent Bessières (IMB), Gérard Besson (IF), Sylvain Maillot (IMAG), Fernando Coda Marques, Laurentbessì Eres, Fernando Marques
(Submitted on 7 Nov 2017)
We prove that the moduli space of complete Riemannian metrics of bounded geometry and uniformly positive scalar curvature on an orientable 3-manifold is path-connected. This generalizes the main result of the fourth author [Mar12] in the compact case. The proof uses Ricci flow with surgery as well as arguments involving performing infinite connected sums with control on the geometry.