$L^\infty$-optimal transport for a class of quasiconvex cost functions

We consider the L∞-optimal mass transportation problem min Π(μ,ν) γ − ess sup c(x, y), for a new class of costs c(x, y) for which we introduce a tentative notion of twist condition. In particular we study the conditions under which the infinitelymotonone transport plans are induced by a transportation map. We also state a uniqueness result for infinitely cyclically monotone Monge minimizers that corresponds to this class of cost functions. We compare the results to previous works.

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