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arXiv · 1505.06789

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

Antonio Ache·Davi Maximo·Haotian Wu
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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.

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Antonio Ache, Davi Maximo, Haotian Wu. 2015-05-26. Metrics with non-negative Ricci curvature on convex three-manifolds. https://doi.org/10.2140/gt.2016.20.2905

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