Curvature Estimates and the Positive Mass Theorem

Details Curvature Estimates and the Positive Mass Theorem Curvature Estimates and the Positive Mass Theorem

1999-06-08

arxiv.org/abs/math/9906047v3

Commun. in Analysis and Geometry 10 (2002) 291-306

Mathematics

Differential Geometry

12 pages, LaTeX (published version)

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Curvature Estimates and the Positive Mass Theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Curvature Estimates and the Positive Mass Theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Curvature Estimates and the Positive Mass Theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-653977