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arXiv · 1808.05064

On optimal transport of matrix-valued measures

Yann Brenier·Dmitry Vorotnikov
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Abstract

We suggest a new way of defining optimal transport of positive-semidefinite matrix-valued measures. It is inspired by a recent rendering of the incompressible Euler equations and related conservative systems as concave maximization problems. The main object of our attention is the Kantorovich-Bures metric space, which is a matricial analogue of the Wasserstein and Hellinger-Kantorovich metric spaces. We establish some topological, metric and geometric properties of this space, which includes the existence of the optimal transportation path.

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Yann Brenier, Dmitry Vorotnikov. 2018-08-15. On optimal transport of matrix-valued measures. https://arxiv.org/abs/1808.05064

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