Rigidity results for initial data sets satisfying the dominant energy condition

Christian Bär; Simon Brendle; Tsz Kiu Aaron Chow; Bernhard Hanke

doi:10.1515/crelle-2025-0080

Rigidity results for initial data sets satisfying the dominant energy condition

Christian Bär
, Simon Brendle^*
, Tsz Kiu Aaron Chow
, Bernhard Hanke

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal Article › peer-review

Abstract

Our work proves rigidity theorems for initial data sets associated with compact smooth spin manifolds with boundary and with compact convex polytopes, subject to the dominant energy condition. For manifolds with smooth boundary, this is based on the solution of a boundary value problem for Dirac operators. For convex polytopes, we use approximations by manifolds with smooth boundary.

Original language	English
Number of pages	43
Journal	Journal fur die Reine und Angewandte Mathematik
DOIs	https://doi.org/10.1515/crelle-2025-0080
Publication status	Published - 8 Nov 2025

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© 2025 the author(s), published by De Gruyter.

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title = "Rigidity results for initial data sets satisfying the dominant energy condition",

abstract = "Our work proves rigidity theorems for initial data sets associated with compact smooth spin manifolds with boundary and with compact convex polytopes, subject to the dominant energy condition. For manifolds with smooth boundary, this is based on the solution of a boundary value problem for Dirac operators. For convex polytopes, we use approximations by manifolds with smooth boundary.",

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AU - Chow, Tsz Kiu Aaron

AU - Hanke, Bernhard

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AB - Our work proves rigidity theorems for initial data sets associated with compact smooth spin manifolds with boundary and with compact convex polytopes, subject to the dominant energy condition. For manifolds with smooth boundary, this is based on the solution of a boundary value problem for Dirac operators. For convex polytopes, we use approximations by manifolds with smooth boundary.

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U2 - 10.1515/crelle-2025-0080

DO - 10.1515/crelle-2025-0080

M3 - Journal Article

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JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

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Rigidity results for initial data sets satisfying the dominant energy condition

Abstract

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