A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds
read the original abstract
The paper establishes a sharp and rigid isoperimetric-type inequality in Lorentzian signature under the assumption of Ricci curvature bounded below in the timelike directions. The inequality is proved in the high generality of Lorentzian pre-length spaces satisfying timelike Ricci lower bounds in a synthetic sense via optimal transport, the so-called $\mathsf{TCD}^e_p(K,N)$ spaces. The results are new already for smooth Lorentzian manifolds. Applications include an upper bound on the area of achronal hypersurfaces inside the interior of a black hole (original already in Schwarzschild) and an upper bound on the area of achronal hypersurfaces in cosmological spacetimes.
This paper has not been read by Pith yet.
Forward citations
Cited by 7 Pith papers
-
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.
-
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.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.