Metrics with nonnegative Ricci curvature on convex three-manifolds

Abstract

We prove that the space of smooth Riemannian metrics on the three-ball with nonnegative Ricci curvature and strictly convex boundary is path-connected, and, moreover, that the associated moduli space (ie modulo orientation-preserving diffeomorphisms of the three-ball) is contractible. As an application, using results of Maximo, Nunes and Smith (to appear in J. Differential Geom.), we show the existence of a properly embedded free boundary minimal annulus on any three-ball with nonnegative Ricci curvature and strictly convex boundary.