Curvature estimates and the Positive Mass Theorem

Journal Article (Journal Article)

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 (ℝ3 δij). 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 (ℝ3, δij), in the sense that there is an upper bound for the L2 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.

Full Text

Duke Authors

Cited Authors

  • Bray, H; Finster, F

Published Date

  • January 1, 2002

Published In

Volume / Issue

  • 10 / 2

Start / End Page

  • 291 - 306

International Standard Serial Number (ISSN)

  • 1019-8385

Digital Object Identifier (DOI)

  • 10.4310/CAG.2002.v10.n2.a3

Citation Source

  • Scopus