# VARIATIONAL HEURISTICS FOR THE MONGE PROBLEM ON COMPACT MANIFOLDS

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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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https://hal.univ-cotedazur.fr/hal-00587919
Contributor : Philippe Delanoë <>
Submitted on : Wednesday, September 28, 2011 - 3:12:01 PM
Last modification on : Monday, October 12, 2020 - 10:27:33 AM
Long-term archiving on: : Thursday, December 29, 2011 - 2:20:48 AM

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• HAL Id : hal-00587919, version 1

### Citation

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

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