@article{73, abstract = {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.}, author = {Erbar, Matthias and Maas, Jan and Wirth, Melchior}, issn = {09442669}, journal = {Calculus of Variations and Partial Differential Equations}, number = {1}, publisher = {Springer}, title = {{On the geometry of geodesics in discrete optimal transport}}, doi = {10.1007/s00526-018-1456-1}, volume = {58}, year = {2019}, }