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Metrics with nonnegative
Ricci curvature on convex three-manifolds
Antonio Aché, Davi Maximo and Haotian Wu |
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Geometry & Topology 20 (2016) 2905–2922
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Abstract |
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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. |
Keywords
moduli space of metrics, gluing positive Ricci curvature,
Ricci flow, manifolds with convex boundary
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Mathematical Subject Classification 2010
Primary: 53C21
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References |
Publication
Received: 1 June 2015
Revised: 3 November 2015
Accepted: 8 November 2015
Published: 7 October 2016
Proposed: John Lott
Seconded: Gang Tian, Bruce Kleiner
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Authors |
| Antonio Aché | |
| Department of Mathematics Princeton University Fine Hall, Washington Road Princeton, NJ 08544-1000 United States |
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| Davi Maximo | |
| Department of Mathematics Stanford University 450 Serra Mall, Building 380 Stanford, CA 94305 United States |
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| Haotian Wu | |
| Department of Mathematics University of Oregon Fenton Hall Eugene, OR 97403 United States |
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