@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},
}