[1] Aleksandr Danilovich Alexandrov. A theorem on triangles in a metric space and some of its applications. Trudy Mat. Inst. Steklov., 38:5-23, 1951.
[2] Jason Altschuler, Jonathan Niles-Weed, and Philippe Rigollet. Near-linear time approximation algorithms for optimal transport via sinkhorn iteration. Advances in neural information processing systems, 30, 2017.
[3] David Alvarez-Melis and Nicolo Fusi. Geometric dataset distances via optimal transport. Advances in Neural Information Processing Systems, 33:21428-21439, 2020.
[4] Luigi Ambrosio, Nicola Gigli, and Giuseppe Savare. Gradient flows: in metric spaces and in the space of probability measures. Springer Science & Business Media, 2005.
[5] Martin Arjovsky, Soumith Chintala, and Léon Bottou. Wasserstein generative adversarial networks. In International conference on machine learning, pages 214-223. PMLR, 2017.
[6] Arturs Backurs, Yihe Dong, Piotr Indyk, Ilya Razenshteyn, and Tal Wagner. Scalable nearest neighbor search for optimal transport. In International Conference on Machine Learning, pages 497-506. PMLR, 2020.
[7] Paul J Besl and Neil D McKay. Method for registration of 3-d shapes. In Sensor fusion IV: control paradigms and data structures, volume 1611, pages 586-606. Spie, 1992.
[8] Garrett Birkhoff. Tres observaciones sobre el algebra lineal. Univ. Nac. Tucuman, Ser. A, 5:147-154, 1946.
[9] Nicolas Bonneel and David Coeurjolly. Spot: sliced partial optimal transport. ACM Transactions on Graphics (TOG), 38(4):1-13, 2019.
[10] Nicolas Bonneel, Julien Rabin, Gabriel Peyre, and Hanspeter Pfister. Sliced and radon wasserstein barycenters of measures. Journal of Mathematical Imaging and Vision, 51(1):22-45, 2015.
[11] Nicolas Bonneel, Michiel Van De Panne, Sylvain Paris, and Wolfgang Heidrich. Displacement interpolation using lagrangian mass transport. In Proceedings of the 2011 SIGGRAPH Asia conference, pages 1-12, 2011.
[12] Yann Brenier. Polar factorization and monotone rearrangement of vector-valued functions. Communications on pure and applied mathematics, 44(4):375-417, 1991.
[13] Giuseppe Buttazzo, Guillaume Carlier, and Katharina Eichinger. Wasserstein interpolation with constraints and application to a parking problem. arXiv preprint arXiv:2207.14261, 2022.
[14] Luis A Caffarelli. Monotonicity properties of optimal transportation and the fkg and related inequalities. Communications in Mathematical Physics, 214(3):547-563, 2000.
[15] Laetitia Chapel, Mokhtar Z Alaya, and Gilles Gasso. Partial optimal transport with applications on positive-unlabeled learning. In Advances in Neural Information Processing Systems, volume 33, pages 2903-2913, 2020.
[16] Rui Chibante. Simulated annealing: theory with applications. BoD-Books on Demand, 2010.
[17] Tarin Clanuwat, Mikel Bober-Irizar, Asanobu Kitamoto, Alex Lamb, Kazuaki Yamamoto, and David Ha. Deep learning for classical japanese literature. In Neural Information Processing Systems Machine Learning for Creativity and Design Workshop, 2018.
[18] Gregory Cohen, Saeed Afshar, Jonathan Tapson, and Andre Van Schaik. EMNIST: Extending MNIST to handwritten letters. In 2017 international joint conference on neural networks (IJCNN), pages 2921-2926, 2017.
[19] Nicolas Courty, Rémi Flamary, Devis Tuia, and Alain Rakotomamonjy. Optimal transport for domain adaptation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 39(9):1853-1865, 2017.