The case of equality for the spacetime positive mass theorem

DOI10.1007/s12220-022-01060-5OpenAlexW4309195137MaRDI QIDQ2105910

Yiyue Zhang, Sven Hirsch

Publication date: 8 December 2022

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.01984

zbMATH Keywords

positive mass theoremharmonic functionsinitial data sets

Mathematics Subject Classification ID

Applications of differential geometry to physics (53Z05) Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory (83C20) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Cites Work

• Proof of the positive mass theorem. II
• On the proof of the positive mass conjecture in general relativity
• The inverse mean curvature flow and the Riemannian Penrose inequality
• A new proof of the positive energy theorem.
• Ricci flow on asymptotically Euclidean manifolds
• Generalized cylinders in semi-Riemannian and spin geometry
• The Jang equation reduction of the spacetime positive energy theorem in dimensions less than eight
• Mass rigidity for hyperbolic manifolds
• Equality in the spacetime positive mass theorem
• The spacetime positive mass theorem in dimensions less than eight
• Killing vectors in asymptotically flat space-times. II. Asymptotically translational Killing vectors and the rigid positive energy theorem in higher dimensions
• Geometric Relativity
• Killing vectors in asymptotically flat space–times. I. Asymptotically translational Killing vectors and the rigid positive energy theorem
• Riemannian Geometry

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