Journal of Dynamics and Differential Equations

, Volume 31, Issue 4, pp 1777–1791 | Cite as

A Geometric Perspective on Regularized Optimal Transport

  • Flavien LégerEmail author


We present new geometric intuition on dynamical versions of regularized optimal transport. We introduce two families of variational problems on Riemannian manifolds which contain analogues of the Schrödinger bridge problem and the Yasue problem. We also propose an analogue of the Hopf–Cole transformation in the geometric setting.


Schrödinger bridge Wasserstein space Optimal transport 



The author would like to thank Alfred Galichon for introducing him to the subject and constant interest in this work, Robert V. Kohn for very helpful comments and Montacer Essid for fruitful discussions.


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Authors and Affiliations

  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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