Introduces ℓ-convergence for Lorentzian pre-length spaces, establishes stability of timelike curvature and CD bounds under it, and derives sharp bounds plus precompactness for generalized cones via GH convergence of bases and fibers.
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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, establishes stability of timelike curvature and CD bounds under it, and derives sharp bounds plus precompactness for generalized cones via GH convergence of bases and fibers.
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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.