On the c-concavity with respect to the quadratic cost on a manifold
Abstract
Pushing a little forward an approach proposed by Villani, we are going to prove that in the Riemannian setting the condition ∇2 f< g implies that f is c-concave with respect to the quadratic cost as soon as it has a sufficiently small C1-norm. From this, we deduce a sufficient condition for the optimality of transport maps.
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