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Stability of a quasi-local positive mass theorem for graphical hypersurfaces of Euclidean space
Department of Mathematics and Computer Science, Clark University, Worcester, Massachusetts; Center of Mathematical Sciences and Applications, Harvard University, Cambridge, Massachusetts.
Department of Mathematics, Universität Tübingen, 72076 Tübingen, Germany.
Matematiska institutionen, Uppsala universitet, 751 06 Uppsala, Sweden.ORCID iD: 0000-0001-9536-9908
2021 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 374, no 5, p. 3535-3555Article in journal (Refereed) Published
Abstract [en]

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 -manifolds with boundary that can be realized as graphs in , 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.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2021. Vol. 374, no 5, p. 3535-3555
National Category
Geometry Mathematical Analysis
Identifiers
URN: urn:nbn:se:ltu:diva-95214DOI: 10.1090/tran/8297ISI: 000636650500015Scopus ID: 2-s2.0-85104237271OAI: oai:DiVA.org:ltu-95214DiVA, id: diva2:1725190
Available from: 2023-01-10 Created: 2023-01-10 Last updated: 2023-05-08Bibliographically approved

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