Optimal transport of vector measures
Functional Analysis
2021-08-17 v1 Metric Geometry
Probability
Abstract
We develop and study a theory of optimal transport for vector measures. We resolve in the negative a conjecture of Klartag, that given a vector measure on Euclidean space with total mass zero, the mass of any transport set is again zero. We provide a counterexample to the conjecture. We generalise the Kantorovich--Rubinstein duality to the vector measures setting. Employing the generalisation, we answer the conjecture in the affirmative provided there exists an optimal transport with absolutely continuous marginals of its total variation.
Keywords
Cite
@article{arxiv.2108.07201,
title = {Optimal transport of vector measures},
author = {Krzysztof J. Ciosmak},
journal= {arXiv preprint arXiv:2108.07201},
year = {2021}
}
Comments
this preprint results from arXiv:1905.02182, which has been split; 26 pages; comments welcome