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Topological Optimization and Optimal Transport by Filippo Santambrogio, Thierry Champion, Guillaume Carlier, Martin Rumpf, Édouard Oudet, Maïtine Bergounioux

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Simone Di Marino, Augusto Gerolin, and Luca Nenna

9 Optimal transportation theory with repulsive costs

Simone Di Marino, Université Paris-Sud, simone.dimarino@math.u-psud.fr

Augusto Gerolin, Dipartimento di Matematica, Università di Pisa, gerolin@mail.dm.unipi.it

Luca Nenna, Inria-Paris, MOKAPLAN, rue Simone Iff, 75012, Paris, France and CEREMADE, UMR CNRS 7534, Université Paris IX Dauphine, luca.nenna@inria.fr

Abstract: This chapter intends to present the state of art and recent developments of the optimal transportation theory with many marginals for a class of repulsive cost functions. We introduce some aspects of the density functional theory (DFT) from a mathematical viewpoint, and revisit the theory of optimal transport from its perspective. ...

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