Simple Unbalanced Optimal Transport
Artikel i vetenskaplig tidskrift, 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.

Författare

Boris Khesin

University of Toronto

Klas Modin

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Göteborgs universitet

Luke Volk

University of Toronto

International Mathematics Research Notices

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

Vol. 2024 10 8839-8855

Långtidsbeteende för tvådimensionella inkompressibla flöden via kvantisering

Vetenskapsrådet (VR) (2022-03453), 2023-01-01 -- 2026-12-31.

Ämneskategorier

Geometri

Matematisk analys

DOI

10.1093/imrn/rnae020

Mer information

Senast uppdaterat

2024-06-01