VARIATIONAL HEURISTICS FOR THE MONGE PROBLEM ON COMPACT MANIFOLDS

Philippe Delanoë (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

We consider the Monge optimal transport problem posed on compact manifolds (possibly with boundary) when all data are smooth and the given measures, positive. If a diffeomorphism is stationary for the total cost, it was established that it must admit a potential function. If it realizes a local minimum of the total cost, we show that the $c$-Hessian of its potential function must be non-negative, positive if we further assume that the cost function $c$ is non degenerate.

Mots clés: Optimal transport; Minimizing diffeomorphism; c-potential; c-Hessian positivity

Domaines: Géométrie différentielle [math.DG]; Equations aux dérivées partielles [math.AP]

Philippe Delanoë. VARIATIONAL HEURISTICS FOR THE MONGE PROBLEM ON COMPACT MANIFOLDS. 2011. ⟨hal-00587919⟩