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Preprints, Working Papers, ... Year : 2011

VARIATIONAL HEURISTICS FOR THE MONGE PROBLEM ON COMPACT MANIFOLDS

Abstract

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.
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Dates and versions

hal-00587919 , version 1 (28-09-2011)

Identifiers

  • HAL Id : hal-00587919 , version 1

Cite

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