Calculus of Variations and Geometric Measure Theory
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F. Glaudo

On the c-concavity with Respect to the Quadratic Cost on a Manifold

created by glaudo on 28 Jan 2018
modified on 28 Mar 2019


Published Paper

Inserted: 28 jan 2018
Last Updated: 28 mar 2019

Journal: Nonlinear Analysis
Volume: 178
Pages: 145-151
Year: 2018


Pushing a little forward an approach proposed by Villani, we are going to prove that in the Riemannian setting the condition $\nabla^2 f<g$ implies that $f$ is $c$-concave with respect to the quadratic cost as soon as it has a sufficiently small $C^1$-norm. From this, we deduce a sufficient condition for the optimality of transport maps.

Keywords: Optimal transport, c-concavity, Riemannian manifold, McCann theorem


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