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Metrics with nonnegative Ricci curvature on convex three-manifolds

Antonio Aché, Davi Maximo and Haotian Wu

Geometry & Topology 20 (2016) 2905–2922

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.

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moduli space of metrics, gluing positive Ricci curvature, Ricci flow, manifolds with convex boundary
Mathematical Subject Classification 2010
Primary: 53C21
Received: 1 June 2015
Revised: 3 November 2015
Accepted: 8 November 2015
Published: 7 October 2016
Proposed: John Lott
Seconded: Gang Tian, Bruce Kleiner
Antonio Aché
Department of Mathematics
Princeton University
Fine Hall, Washington Road
Princeton, NJ 08544-1000
United States
Davi Maximo
Department of Mathematics
Stanford University
450 Serra Mall, Building 380
Stanford, CA 94305
United States
Haotian Wu
Department of Mathematics
University of Oregon
Fenton Hall
Eugene, OR 97403
United States