Work

Centroids for weak optimal transport with barycentric cost

Year: 2026

Type: preprint

Abstract: We generalize the theory of Wasserstein barycenters between N given measures from the Wasserstein distance to the weak optimal transport problem with barycentric cost. We find a multi-marginal formulation and its dual problem. The multi-marginal problem is new in itself; contrary to the classical multi-marginal optimal transport problem, the first M marginals of its competitors are not fixed but instead only need dominate the first M given measures in convex order, while the last N-M marginals of its competitors are dominated in convex order by the last N-M given measures.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.17784

Author: Krannich, Friedemann

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Natural Sciences and Engineering Research Council of Canada

Awards: G2271590008, G4221773844, Mathematics, Economics and Physics, Variational problems in physics, economics and geometry

OpenAlex ID: W7213502095

Cites: 2

Cited by:

Related to: 10