Causally simple spacetimes with continuous Lorentzian metrics on smooth manifolds are infinitesimally Minkowskian.
A sharp isoperimetric-type inequal- ity for Lorentzian spaces satisfying timelike Ricci lower bounds
6 Pith papers cite this work. Polarity classification is still indexing.
6
Pith papers citing it
citation-role summary
background 1
citation-polarity summary
verdicts
UNVERDICTED 6roles
background 1polarities
background 1representative citing papers
Rigidity theorem for the Borell-Brascamp-Lieb inequality is shown on weighted Riemannian manifolds, generalizing Balogh-Kristály to the weighted setting.
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.
Under the strong energy condition, positive lower bounds on asymptotic volume-expansion invariants imply past timelike geodesic incompleteness with explicit time bound; extends to synthetic TCD^e_p(0,N) length spaces.
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.
citing papers explorer
-
Infinitesimal Minkowskianity for manifolds with continuous Lorentzian metrics
Causally simple spacetimes with continuous Lorentzian metrics on smooth manifolds are infinitesimally Minkowskian.
-
Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds
Rigidity theorem for the Borell-Brascamp-Lieb inequality is shown on weighted Riemannian manifolds, generalizing Balogh-Kristály to the weighted setting.
-
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.
-
A singularity theorem in terms of asymptotic expansion
Under the strong energy condition, positive lower bounds on asymptotic volume-expansion invariants imply past timelike geodesic incompleteness with explicit time bound; extends to synthetic TCD^e_p(0,N) length spaces.
-
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.