The Monge problem for supercritical Mañé potentials on compact manifolds
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چکیده
We prove the existence of optimal transport maps for the Monge problem when the cost is a Finsler distance on a compact manifold. Our point of view consists in considering the distance as a Mañé potential, and to rely on recent developments in the theory of viscosity solutions of the Hamilton-Jacobi equation. Résumé: On montre l’existence d’une application de transport optimale pour le problème de Monge lorsque le cout est une distance Finslerienne sur une variété compacte. Le nouveau point de vue consiste à considérer la distance comme un potentiel de Mañé, et à exploiter des développements récents sur les solutions de viscostité de l’équation de Hamilton-Jacobi. Patrick Bernard Institut Fourier, Grenoble, on move to CEREMADE Université de Paris Dauphine Pl. du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16 France [email protected] Boris Buffoni School of Mathematics École Polytechnique Fédérale-Lausanne SB/IACS/ANA Station 8 1015 Lausanne Switzerland [email protected]
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تاریخ انتشار 2005