Deforming 3-manifolds of bounded geometry and uniformly positive scalar curvature

2017/11/07 by Laurent Bessières, Gérard Besson, Bessières, Laurent +5 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1711.02457

openalex publication_date 2017/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• A Compactness Property for Solutions of the Ricci Flow
• Existence of Incompressible Minimal Surfaces and the Topology of Three Dimensional Manifolds with Non-Negative Scalar Curvature

Cited by

• Positive curvature conditions on contractible manifolds

Related

• Deforming three-manifolds with positive scalar curvature
• Constrained deformations of positive scalar curvature metrics
• 3-Manifolds with positive scalar curvature and bounded geometry
• On the Moduli Space of Asymptotically Flat Manifolds with Boundary and the Constraint Equations
• Mean Curvature Flow and Heegaard Surfaces in Lens Spaces