Math @ Duke

Publications [#287086] of Hubert Bray
Papers Published
 Bray, H; Finster, F, Curvature estimates and the Positive Mass Theorem,
Communications in Analysis and Geometry, vol. 10 no. 2
(January, 2002),
pp. 291306, International Press of Boston [arXiv:math/9906047v3], [doi]
(last updated on 2019/07/24)
Abstract: The Positive Mass Theorem implies that any smooth, complete, asymptotically flat 3manifold with nonnegative 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 nonnegative 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 nonsmooth manifolds with generalized nonnegative scalar curvature, which we define.


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