Metrics with nonnegative Ricci curvature on convex three-manifolds
| Autor: | Antonio G. Ache, Haotian Wu, Davi Maximo |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Mathematics - Differential Geometry
0209 industrial biotechnology Pure mathematics manifolds with convex boundary Boundary (topology) 53C21 02 engineering and technology Space (mathematics) 01 natural sciences Contractible space gluing positive Ricci curvature moduli space of metrics Mathematics - Geometric Topology 020901 industrial engineering & automation Ricci flow FOS: Mathematics 0101 mathematics Ricci curvature Mathematics 010102 general mathematics Geometric Topology (math.GT) Annulus (mathematics) Moduli space Differential Geometry (math.DG) Mathematics::Differential Geometry Geometry and Topology Convex function |
| Zdroj: | Geom. Topol. 20, no. 5 (2016), 2905-2922 |
| ISSN: | 1364-0380 1465-3060 |
| DOI: | 10.2140/gt.2016.20.2905 |
| Popis: | 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. Strengthened the conclusions in Theorems 1.1 and 1.2 that the respective moduli spaces are contractible; corrected typos; updated references. To appear in Geometry & Topology |
| Databáze: | OpenAIRE |
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