$h$-Wasserstein barycenters
Analysis of PDEs
2024-02-21 v1
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 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 -point configurations to their -barycenter on the support of an optimal multi-marginal plan.
Cite
@article{arxiv.2402.13176,
title = {$h$-Wasserstein barycenters},
author = {Camilla Brizzi and Gero Friesecke and Tobias Ried},
journal= {arXiv preprint arXiv:2402.13176},
year = {2024}
}