10.1007/s00526-018-1456-1
Erbar, Matthias
Matthias
Erbar
Maas, Jan
Jan
Maas0000-0002-0845-1338
Wirth, Melchior
Melchior
Wirth
On the geometry of geodesics in discrete optimal transport
Springer
2019
2018-12-11T11:44:29Z
2020-01-21T13:22:12Z
journal_article
/record/73
/record/73.json
09442669
1805.06040
645565 bytes
application/pdf
We consider the space of probability measures on a discrete set X, endowed with a dynamical optimal transport metric. Given two probability measures supported in a subset Y⊆X, it is natural to ask whether they can be connected by a constant speed geodesic with support in Y at all times. Our main result answers this question affirmatively, under a suitable geometric condition on Y introduced in this paper. The proof relies on an extension result for subsolutions to discrete Hamilton-Jacobi equations, which is of independent interest.