The Monge problem for supercritical Mañé potentials on compact manifolds

• Autores: Patrick Bernard, Boris Buffoni
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 207, Nº 2, 2006, págs. 691-706
• Idioma: inglés
• DOI: 10.1016/j.aim.2006.01.003
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• Resumen

  • 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.