Introduces ℓ-convergence for Lorentzian pre-length spaces with stability of timelike curvature bounds, applies it to generalized cones for sharp bounds, and proves precompactness under uniform Ricci/Riemann bounds.
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The paper reviews progress on geometric stability of the zero ADM mass rigidity theorem and states that it remains an open question which notion of geometric convergence best captures this stability even in three dimensions.
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Convergence of Lorentzian spaces and curvature bounds for generalized cones
Introduces ℓ-convergence for Lorentzian pre-length spaces with stability of timelike curvature bounds, applies it to generalized cones for sharp bounds, and proves precompactness under uniform Ricci/Riemann bounds.
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Geometric Stability of the Schoen-Yau Zero Mass Theorem
The paper reviews progress on geometric stability of the zero ADM mass rigidity theorem and states that it remains an open question which notion of geometric convergence best captures this stability even in three dimensions.