2024
DOI: 10.1093/imrn/rnae020
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Simple Unbalanced Optimal Transport

Boris Khesin,
Klas Modin,
Luke Volk

Abstract: We introduce and study a simple model capturing the main features of unbalanced optimal transport. It is based on equipping the conical extension of the group of all diffeomorphisms with a natural metric, which allows a Riemannian submersion to the space of volume forms of arbitrary total mass. We describe its finite-dimensional version and present a concise comparison study of the geometry, Hamiltonian features, and geodesics for this and other extensions. One of the corollaries of this approach is that along… Show more

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