On the geometry of geodesics in discrete optimal transport Preprint


Author(s): Erbar, Matthias; Maas, Jan; Wirth, Melchior
Title: On the geometry of geodesics in discrete optimal transport
Affiliation IST Austria
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.
Publication Title: ArXiv
Publisher: ArXiv  
Date Published: 2018-05-31
URL:
Open access: yes (repository)
IST Austria Authors
  1. Jan Maas
    28 Maas
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