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.
McCann, Argam Ohanyan, Felix Rott, and Clemens S¨ amann
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A coarea inequality holds for Lorentzian Hausdorff measure via diameter-preserving maps on causal pre-length spaces together with a covering lemma under local causal enlargement.
Causally simple spacetimes with continuous Lorentzian metrics on smooth manifolds are infinitesimally Minkowskian.
In synthetic Lorentzian spaces, the timelike curvature dimension condition TCD_q(K,N) is equivalent to the timelike Brunn-Minkowski inequality TBM_q(K,N) in the q-essentially non-branching case, with a similar equivalence for the entropic version.
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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
A coarea inequality holds for Lorentzian Hausdorff measure via diameter-preserving maps on causal pre-length spaces together with a covering lemma under local causal enlargement.
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Infinitesimal Minkowskianity for manifolds with continuous Lorentzian metrics
Causally simple spacetimes with continuous Lorentzian metrics on smooth manifolds are infinitesimally Minkowskian.
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The equivalence between timelike Ricci curvature and the timelike Brunn Minkowski inequality on synthetic Lorentzian spaces
In synthetic Lorentzian spaces, the timelike curvature dimension condition TCD_q(K,N) is equivalent to the timelike Brunn-Minkowski inequality TBM_q(K,N) in the q-essentially non-branching case, with a similar equivalence for the entropic version.
- Timelike Ricci curvature lower bounds via optimal transport for Orlicz-type Lorentzian costs