Equivalence shown between magnetic Brunn-Minkowski inequalities for geodesic interpolation and magnetic Ricci curvature lower bounds, plus sharp example on Heisenberg group.
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9 Pith papers cite this work. Polarity classification is still indexing.
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Defines Ollivier-Ricci curvature for causal sets using Lorentzian optimal transport, proves local-to-global and Bonnet-Myers results, and validates numerically on sprinkled constant-curvature 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.
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.
citing papers explorer
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Magnetic Brunn-Minkowski inequalities
Equivalence shown between magnetic Brunn-Minkowski inequalities for geodesic interpolation and magnetic Ricci curvature lower bounds, plus sharp example on Heisenberg group.
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Ollivier-Ricci Curvature for Causal Sets
Defines Ollivier-Ricci curvature for causal sets using Lorentzian optimal transport, proves local-to-global and Bonnet-Myers results, and validates numerically on sprinkled constant-curvature spacetimes.
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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.
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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.
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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.
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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.
- Stability of Synthetic Timelike Ricci Bounds under $C^0$-Limits and Applications to Impulsive Gravitational Waves
- Hausdorff-type metric geometry of the space of Cauchy hypersurfaces