Curvature Estimates and the Positive Mass Theorem
| dc.creator | Bray, Hubert | |
| dc.creator | Finster, Felix | |
| dc.date | 1999-06-08 | |
| dc.date | 2000-05-16 | |
| dc.date.accessioned | 2026-07-07T05:29:24Z | |
| dc.date.available | 2026-07-07T05:29:24Z | |
| dc.description | The Positive Mass Theorem implies that any smooth, complete, asymptotically flat 3-manifold with non-negative scalar curvature which has zero total mass is isometric to (R^3, delta_{ij}). In this paper, we quantify this statement using spinors and prove that if a complete, asymptotically flat manifold with non-negative scalar curvature has small mass and bounded isoperimetric constant, then the manifold must be close to (R^3,delta_{ij}), in the sense that there is an upper bound for the L^2 norm of the Riemannian curvature tensor over the manifold except for a set of small measure. This curvature estimate allows us to extend the case of equality of the Positive Mass Theorem to include non-smooth manifolds with generalized non-negative scalar curvature, which we define. | |
| dc.description | 12 pages, LaTeX (published version) | |
| dc.identifier | https://arxiv.org/abs/math/9906047 | |
| dc.identifier | http://arxiv.org/abs/math/9906047 | |
| dc.identifier | Commun. in Analysis and Geometry 10 (2002) 291-306 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78627 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.title | Curvature Estimates and the Positive Mass Theorem | |
| dc.type | text |