Published Paper

Inserted: 7 mar 2024
Last Updated: 22 oct 2025

Journal: Journal of Mathematical Analysis and Applications
Volume: 553
Year: 2026
Doi: 10.1016/j.jmaa.2025.129952

Abstract:

We generalize the notion and theory of Wasserstein barycenters introduced by Agueh and Carlier (2011) from the quadratic cost to general smooth strictly convex costs $h$ with non-degenerate Hessian. We show the equivalence between a coupled two-marginal and a multi-marginal formulation and establish that the multi-marginal optimal plan is unique and of Monge form. To establish the latter result we introduce a new approach which is not based on explicitly solving the optimality system, but instead deriving a quantitative injectivity estimate for the (highly non-injective) map from $N$-point configurations to their $h$-barycenter on the support of an optimal multi-marginal plan.