Strong c-concavity and stability in optimal transport

@article{Gallout2022StrongCA,
  title={Strong c-concavity and stability in optimal transport},
  author={Anatole Gallou{\"e}t and Quentin M'erigot and Boris Thibert},
  journal={ArXiv},
  year={2022},
  volume={abs/2207.11042}
}
. The stability of solutions to optimal transport problems under variation of the measures is fundamental from a mathematical view-point: it is closely related to the convergence of numerical approaches to solve optimal transport problems and justifies many of the applications of optimal transport. In this article, we introduce the notion of strong c -concavity, and we show that it plays an important role for proving stability results in optimal transport for general cost functions c . We then… 

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