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Almost Rigidity of the Positive Mass Theorem

Banff International Research Station for Mathematical Innovation and Discovery

The Positive Mass Theorem includes a rigidity statement that an asymptotically flat manifold with nonnegative scalar curvature and 0 ADM mass is Euclidean space. The correspond- ing almost rigidity statement that a sequence of asymptotically flat manifolds with nonnegative scalar curvature whose ADM mass converges to 0 should converge in some sense to Euclidean space has only been proven in some settings. I will survey recent results in special settings jointly with Lee, with Huang and Lee, and with Stavrov in which it has been shown that one obtains convergence in the intrinsic flat sense. Intrinsic Flat convergence will be defined and a theorem with Lakzian which allows one to prove intrinsic flat convergence will be presented as well.

Mathematics; Relativity and gravitational theory; Differential geometry

video/mp4

Author affiliation: City University of New York

2017-02-05

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60379

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/