Journal
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
Volume 727, Issue -, Pages 269-299Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/crelle-2015-0051
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Funding
- NSF [0932078 000, DMS 1308837, DMS 1452477, DMS 1309360]
- PSC CUNY Research Grant
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1309360] Funding Source: National Science Foundation
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The rigidity of the Positive Mass Theorem states that the only complete asymptotically flat manifold of nonnegative scalar curvature and zero mass is Euclidean space. We study the stability of this statement for spaces that can be realized as graphical hypersurfaces in En+1. We prove (under certain technical hypotheses) that if a sequence of complete asymptotically flat graphs of nonnegative scalar curvature has mass approaching 0, then the sequence must converge to Euclidean space in the pointed intrinsic flat sense. The appendix includes a new Gromov-Hausdorff and intrinsic flat compactness theorem for sequences of metric spaces with uniform Lipschitz bounds on their metrics.
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