On the geometry of geodesics in discrete optimal transport

M. Erbar, J. Maas, M. Wirth, Calculus of Variations and Partial Differential Equations 58 (2019).

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Journal Article | Published | English
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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.
Publishing Year
Date Published
2019-02-01
Journal Title
Calculus of Variations and Partial Differential Equations
Acknowledgement
Open access funding provided by Institute of Science and Technology (IST Austria)
Volume
58
Issue
1
Article Number
19
ISSN
IST-REx-ID

Cite this

Erbar M, Maas J, Wirth M. On the geometry of geodesics in discrete optimal transport. Calculus of Variations and Partial Differential Equations. 2019;58(1). doi:10.1007/s00526-018-1456-1
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). https://doi.org/10.1007/s00526-018-1456-1
Erbar, Matthias, Jan Maas, and Melchior Wirth. “On the Geometry of Geodesics in Discrete Optimal Transport.” Calculus of Variations and Partial Differential Equations 58, no. 1 (2019). https://doi.org/10.1007/s00526-018-1456-1.
M. Erbar, J. Maas, and M. Wirth, “On the geometry of geodesics in discrete optimal transport,” Calculus of Variations and Partial Differential Equations, vol. 58, no. 1, 2019.
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).
Erbar, Matthias, et al. “On the Geometry of Geodesics in Discrete Optimal Transport.” Calculus of Variations and Partial Differential Equations, vol. 58, no. 1, 19, Springer, 2019, doi:10.1007/s00526-018-1456-1.
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