Simple Unbalanced Optimal Transport
Journal article, 2024

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 any geodesic the total mass evolves with constant acceleration, as an object's height in a constant buoyancy field.

Author

Boris Khesin

University of Toronto

Klas Modin

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Luke Volk

University of Toronto

International Mathematics Research Notices

1073-7928 (ISSN) 1687-0247 (eISSN)

Vol. 2024 10 8839-8855

Long-time 2D hydrodynamics via quantization

Swedish Research Council (VR) (2022-03453), 2023-01-01 -- 2026-12-31.

Subject Categories

Geometry

Mathematical Analysis

DOI

10.1093/imrn/rnae020

More information

Latest update

6/1/2024 4