Metrics with non-negative Ricci curvature on convex three-manifolds

Abstract

We prove that the space of smooth Riemannian metrics on the three-ball with non-negative Ricci curvature and strictly convex boundary is path connected; and, moreover, that the associated moduli space (i.e., modulo orientation-preserving diffeomorphisms of the three-ball) is contractible. As an application, using results of Maximo, Nunes, and Smith [MNS13], we show the existence of properly embedded free boundary minimal annulus on any three-ball with non-negative Ricci curvature and strictly convex boundary.

Strengthened the conclusions in Theorems 1.1 and 1.2 that the respective moduli spaces are contractible; corrected typos; updated references. To appear in Geometry & Topology

References in corpus (2)

• The space of metrics of positive scalar curvature
• Mean curvature flow in a Ricci flow background

Cited by in corpus (2)

• Ricci-Positive Metrics on Connected Sums of Projective Spaces
• The growth rate of harmonic functions