Synthetic timelike Ricci bounds TCD^e_p(K,N) are stable under C^0-limits of Lorentzian metrics, with applications to impulsive gravitational waves and counterexamples to Lorentzian splitting theorems.
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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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Stability of Synthetic Timelike Ricci Bounds under $C^0$-Limits and Applications to Impulsive Gravitational Waves
Synthetic timelike Ricci bounds TCD^e_p(K,N) are stable under C^0-limits of Lorentzian metrics, with applications to impulsive gravitational waves and counterexamples to Lorentzian splitting theorems.
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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.