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 locally uniformly d-controlling maps preserving causal diamond diameters and proves the coarea inequality for Lorentzian Hausdorff measure in pre-length spaces, plus a covering lemma under local causal enlargement.
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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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Lorentzian coarea inequality
Introduces locally uniformly d-controlling maps preserving causal diamond diameters and proves the coarea inequality for Lorentzian Hausdorff measure in pre-length spaces, plus a covering lemma under local causal enlargement.