Intrinsic flat convergence of points and applications to stability of the positive mass theorem

2020/10/15 by Huang, Lan-Hsuan, Lee, Dan A., Perales, Raquel · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2010.07885

Abstract

We prove results on intrinsic flat convergence of points---a concept first explored by Sormani in \citeSormani-AA. In particular, we discuss compatibility with Gromov-Hausdorff convergence of points---a concept first described by Gromov in \citeGromov-poly. We apply these results to the problem of stability of the positive mass theorem in mathematical relativity. Specifically, we revisit the article \citeHLS on intrinsic flat stability for the case of graphical hypersurfaces of Euclidean space: We are able to fill in some details in the proofs of Theorems 1.4 and Lemma~5.1 of \citeHLS and strengthen some statements. Moreover, in light of an acknowledged error in the proof of Theorem~1.3 of \citeHLS, we provide an alternative proof that extends recent work of \citeAP20.

Cited by

• Metric Convergence of Sequences of Static Spacetimes with the Null Distance

Related

• Intrinsic flat stability of the positive mass theorem for graphical hypersurfaces of Euclidean space
• Rigidity of positive mass theorem with fast metric decay
• Notes on Pointed Gromov-Hausdorff Convergence
• Properties of the Intrinsic Flat Distance
• Intrinsic flat stability of the positive mass theorem for asymptotically hyperbolic graphical manifolds