On the sparsity of h-Wasserstein barycenters

In my talk I will briefly present the multi-marginal optimal transport problem of finding the h-Wasserstein barycenter, where h is a nonnegative strictly convex function, as a generalization of the better known 2-Wasserstein barycenter. It appeared for the first time in a work by Argueh and Carlier and was further studied by Pass. The focus of the talk is the sparsity of the optimal plan for the MMOT formulation, which for the 2-case has been proved by Gangbo and Święch. Here we provide a proof of the absolute continuity of the h-Waserstein barycenter, which implies that the optimal plan is of Monge type.

This is a joint ongoing work together with G. Friesecke and T. Ried.