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.
A nonlinear d’Alembert comparison theorem and causal differential calculus on metric measure spacetimes
9 Pith papers cite this work. Polarity classification is still indexing.
9
Pith papers citing it
citation-role summary
background 1
citation-polarity summary
verdicts
UNVERDICTED 9roles
background 1polarities
background 1representative citing papers
Timelike Ricci curvature lower bounds are characterized by convexity of relative entropy along geodesics in optimal transport with general Orlicz-type Lorentzian costs u composed with time separation on globally hyperbolic spacetimes.
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.
An analogue of Reshetnyak's majorisation theorem is proven for Lorentzian length spaces with upper curvature bounds, yielding a four-point characterization of those bounds suitable for discrete settings.
Introduces a synthetic null energy condition using optimal transport on topological causal spaces that agrees with the classical NEC in smooth cases and enables proofs of area and singularity theorems in non-smooth settings.
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.
Proves diffeomorphic splitting for timelike geodesically complete weighted Finsler spacetimes and isometry generation for Berwald cases via the p-d'Alembertian, generalizing prior Lorentzian results.
Introduces a measure-dependent relaxation of bounded-length-distortion and establishes existence of such maps from finite-Hausdorff-dimension metric measure spaces into finite-dimensional normed spaces.
citing papers explorer
-
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.
-
Timelike Ricci curvature lower bounds via optimal transport for Orlicz-type Lorentzian costs
Timelike Ricci curvature lower bounds are characterized by convexity of relative entropy along geodesics in optimal transport with general Orlicz-type Lorentzian costs u composed with time separation on globally hyperbolic spacetimes.
-
Infinitesimal Minkowskianity for manifolds with continuous Lorentzian metrics
Causally simple spacetimes with continuous Lorentzian metrics on smooth manifolds are infinitesimally Minkowskian.
-
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.
-
Reshetnyak Majorisation and discrete upper curvature bounds for Lorentzian length spaces
An analogue of Reshetnyak's majorisation theorem is proven for Lorentzian length spaces with upper curvature bounds, yielding a four-point characterization of those bounds suitable for discrete settings.
-
On the geometry of synthetic null hypersurfaces
Introduces a synthetic null energy condition using optimal transport on topological causal spaces that agrees with the classical NEC in smooth cases and enables proofs of area and singularity theorems in non-smooth settings.
-
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.
-
Splitting theorems for weighted Finsler spacetimes via the $p$-d'Alembertian: beyond the Berwald case
Proves diffeomorphic splitting for timelike geodesically complete weighted Finsler spacetimes and isometry generation for Berwald cases via the p-d'Alembertian, generalizing prior Lorentzian results.
-
On one relaxation of the bounded-length-distortion condition in the context of metric measure spaces
Introduces a measure-dependent relaxation of bounded-length-distortion and establishes existence of such maps from finite-Hausdorff-dimension metric measure spaces into finite-dimensional normed spaces.