Curvature Estimates and the Positive Mass Theorem

dc.creatorBray, Hubert
dc.creatorFinster, Felix
dc.date1999-06-08
dc.date2000-05-16
dc.date.accessioned2026-07-07T05:29:24Z
dc.date.available2026-07-07T05:29:24Z
dc.descriptionThe 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.description12 pages, LaTeX (published version)
dc.identifierhttps://arxiv.org/abs/math/9906047
dc.identifierhttp://arxiv.org/abs/math/9906047
dc.identifierCommun. in Analysis and Geometry 10 (2002) 291-306
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78627
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.titleCurvature Estimates and the Positive Mass Theorem
dc.typetext

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