Energy and volume: A proof of the positivity of ADM energy using the yamabe invariant of three-manifolds

DOI10.1007/s00220-008-0711-2zbMath1172.53046OpenAlexW2029475981MaRDI QIDQ842452

Martin Reiris

Publication date: 25 September 2009

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00220-008-0711-2

zbMATH Keywords

maximally expanding compact cosmologiessigma constantThurston geometrization of three-manifolds Yamabe invariant

Mathematics Subject Classification ID

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)

Related Items (1)

The Ricci flow of asymptotically hyperbolic mass and applications

Cites Work

• A complete proof of the Poincaré and geometrization conjectures -- application of the Hamilton-Perelman theory of the Ricci flow
• Proof of the positive mass theorem. II
• On the proof of the positive mass conjecture in general relativity
• Scalar curvature and hammocks
• The inverse mean curvature flow and the Riemannian Penrose inequality
• A new proof of the positive energy theorem.
• Canonical metrics on 3-manifolds and 4-manifolds
• The Yamabe problem
• A Unique Decomposition Theorem for 3-Manifolds
• General {\cal K}=-1 Friedman–Lemaître models and the averaging problem in cosmology
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