In globally hyperbolic spacetimes, the locus of multiple maximizing geodesics is locally contractible and homotopy equivalent to the causal future minus the Lorentzian Aubry set.
$C_{loc}^{1,1}$ optimal pairs in the dual optimal transport problem for a Lorentzian cost along displacement interpolations
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We consider the optimal transportation problem on a globally hyperbolic spacetime with a cost function $c$, which corresponds to the optimal transportation problem on a complete Riemannian manifold where the cost function is given by the squared Riemannian distance. Building upon methods of weak KAM theory, we will establish the existence of $C_{loc}^{1,1}$ optimal pairs for the dual optimal transport problem for probability measures along displacement interpolations.
citation-role summary
background 1
citation-polarity summary
fields
math.OC 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
background 1representative citing papers
citing papers explorer
-
On the locus of multiple maximizing geodesics on a globally hyperbolic spacetime
In globally hyperbolic spacetimes, the locus of multiple maximizing geodesics is locally contractible and homotopy equivalent to the causal future minus the Lorentzian Aubry set.