A spacetime positive mass theorem with corners via mollification

2026/07/21 by Hyun Chul Jang, Aidan F. Wood
#math.DG #gr-qc

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Abstract

We prove a strict dominant energy deformation theorem for asymptotically flat initial data with corners along a hypersurface Σ. The deformation preserves a corner condition on the Bartnik data across Σ. We show that if the dominant energy condition holds on each side of Σ and the Bartnik data satisfy this corner condition, then the exterior end satisfies E ≥ |P| in every dimension n ≥ 3.

Citations

• The mass of an asymptotically flat manifold
• On the proof of the positive mass conjecture in general relativity

Related

• On a spacetime positive mass theorem with corners
• A tilted spacetime positive mass theorem
• The spacetime positive mass theorem in dimensions less than eight
• Positive mass theorem for initial data sets with corners along a hypersurface
• Tilted spacetime positive mass theorem with arbitrary ends