6 papers
Lipschitz continuity of the cut time for globally hyperbolic spacetimes
Alec Metsch
We prove that, for a fixed point in a globally hyperbolic spacetime, the focalization time is locally Lipschitz continuous on the open subset of the future causal cone where it is…
A Lorentzian Lasry-Lions regularization theorem
Alec Metsch
The main goal of this paper is to establish a general Lorentzian Lasry-Lions regularization theorem: let be a function defined on a globally hyperbolic spacetime. Assume that i…
Semiconvexity of (weak) Kantorovich potentials in the Lorentzian optimal transport problem
Alec Metsch
We study semiconvexity properties of (weak) Kantorovich potentials for the Lorentzian optimal transport problem with the standard cost function . We show that, in general, this…
On the locus of multiple maximizing geodesics on a globally hyperbolic spacetime
Alec Metsch
Extending the recent work of Cannarsa, Cheng and Fathi, we investigate topological properties of the locus of multiple maximizing geodesics on a globally hyperboli…
optimal pairs in the dual optimal transport problem for a Lorentzian cost along displacement interpolations
Alec Metsch
We consider the optimal transportation problem on a globally hyperbolic spacetime with a cost function , which corresponds to the optimal transportation problem on a complete Ri…
Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime
Alec Metsch
We consider the optimal transportation problem on a globally hyperbolic spacetime for some cost function , which corresponds to the optimal transportation problem on a complet…