---
_id: '73'
abstract:
- lang: eng
  text: 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.
article_number: '19'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Matthias
  full_name: Erbar, Matthias
  last_name: Erbar
- first_name: Jan
  full_name: Maas, Jan
  id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
  last_name: Maas
  orcid: 0000-0002-0845-1338
- first_name: Melchior
  full_name: Wirth, Melchior
  last_name: Wirth
citation:
  ama: Erbar M, Maas J, Wirth M. On the geometry of geodesics in discrete optimal
    transport. <i>Calculus of Variations and Partial Differential Equations</i>. 2019;58(1).
    doi:<a href="https://doi.org/10.1007/s00526-018-1456-1">10.1007/s00526-018-1456-1</a>
  apa: Erbar, M., Maas, J., &#38; Wirth, M. (2019). On the geometry of geodesics in
    discrete optimal transport. <i>Calculus of Variations and Partial Differential
    Equations</i>. Springer. <a href="https://doi.org/10.1007/s00526-018-1456-1">https://doi.org/10.1007/s00526-018-1456-1</a>
  chicago: Erbar, Matthias, Jan Maas, and Melchior Wirth. “On the Geometry of Geodesics
    in Discrete Optimal Transport.” <i>Calculus of Variations and Partial Differential
    Equations</i>. Springer, 2019. <a href="https://doi.org/10.1007/s00526-018-1456-1">https://doi.org/10.1007/s00526-018-1456-1</a>.
  ieee: M. Erbar, J. Maas, and M. Wirth, “On the geometry of geodesics in discrete
    optimal transport,” <i>Calculus of Variations and Partial Differential Equations</i>,
    vol. 58, no. 1. Springer, 2019.
  ista: Erbar M, Maas J, Wirth M. 2019. On the geometry of geodesics in discrete optimal
    transport. Calculus of Variations and Partial Differential Equations. 58(1), 19.
  mla: Erbar, Matthias, et al. “On the Geometry of Geodesics in Discrete Optimal Transport.”
    <i>Calculus of Variations and Partial Differential Equations</i>, vol. 58, no.
    1, 19, Springer, 2019, doi:<a href="https://doi.org/10.1007/s00526-018-1456-1">10.1007/s00526-018-1456-1</a>.
  short: M. Erbar, J. Maas, M. Wirth, Calculus of Variations and Partial Differential
    Equations 58 (2019).
date_created: 2018-12-11T11:44:29Z
date_published: 2019-02-01T00:00:00Z
date_updated: 2023-09-13T09:12:35Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00526-018-1456-1
ec_funded: 1
external_id:
  arxiv:
  - '1805.06040'
  isi:
  - '000452849400001'
file:
- access_level: open_access
  checksum: ba05ac2d69de4c58d2cd338b63512798
  content_type: application/pdf
  creator: dernst
  date_created: 2019-01-28T15:37:11Z
  date_updated: 2020-07-14T12:47:55Z
  file_id: '5895'
  file_name: 2018_Calculus_Erbar.pdf
  file_size: 645565
  relation: main_file
file_date_updated: 2020-07-14T12:47:55Z
has_accepted_license: '1'
intvolume: '        58'
isi: 1
issue: '1'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '716117'
  name: Optimal Transport and Stochastic Dynamics
- _id: 260482E2-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: ' F06504'
  name: Taming Complexity in Partial Di erential Systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: Calculus of Variations and Partial Differential Equations
publication_identifier:
  issn:
  - '09442669'
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the geometry of geodesics in discrete optimal transport
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 58
year: '2019'
...