Metrics with Non-negative Ricci Curvature on Convex Three-manifolds
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چکیده
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 threeball) is contractible. As an application, using results of Maximo, Nunes, and Smith [MNS], we show the existence of properly embedded free boundary minimal annulus on any three-ball with non-negative Ricci curvature and strictly convex boundary.
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تاریخ انتشار 2015