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The Monge problem for supercritical Mane potentials on compact manifolds

Patrick Bernard·Boris Buffoni
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Abstract

We prove the existence of an optimal map for the Monge problem when the cost is a supercritical Mane potential on a compact manifold. Supercritical Mane potentials form a class of costs which generalize the Riemannian distances. We describe new links between this transportation problem and viscosity subsolutions of the Hamilton-Jacobi equation.

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Patrick Bernard, Boris Buffoni. 2007-01-16. The Monge problem for supercritical Mane potentials on compact manifolds. https://arxiv.org/abs/math/0502136

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