L∞-optimal transport for a class of strictly quasiconvex cost functions

We consider the L-infinity-optimal mass transportation problem min(Pi(mu,nu)) gamma - 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 infinity-monotone 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. (c) 2023 Published by Elsevier Inc.