Mathematics
Stability of a quasi-local positive mass theorem for graphical hypersurfaces of euclidean space
Document Type
Article
Abstract
We present a quasi-local version of the stability of the positive mass theorem. We work with the Brown-York quasi-local mass as it possesses positivity and rigidity properties, and therefore the stability of this rigidity statement can be studied. Specifically, we ask if the Brown-York mass of the boundary of some compact manifold is close to zero, must the manifold be close to a Euclidean domain in some sense? Here we consider a class of compact n-manifolds with boundary that can be realized as graphs in Rn+1, and establish the following. If the Brown-York mass of the boundary of such a compact manifold is small, then the manifold is close to a Euclidean hyperplane with respect to the Federer-Fleming flat distance.
Publication Title
Transactions of the American Mathematical Society
Publication Date
5-2021
Volume
374
Issue
5
First Page
3535
Last Page
3555
ISSN
0002-9947
DOI
10.1090/tran/8297
Keywords
black holes, initial datum, manifold
Repository Citation
Alaee, Aghil; Cabrera Pacheco, Armando J.; and McCormick, Stephen, "Stability of a quasi-local positive mass theorem for graphical hypersurfaces of euclidean space" (2021). Mathematics. 46.
https://commons.clarku.edu/mathematics/46
