@article{Brenier1991,
  author = {Yann Brenier},
  title = {Polar factorization and monotone rearrangement of vector-valued functions},
  journal = {Communications on Pure and Applied Mathematics},
  volume = {44},
  number = {4},
  pages = {375--417},
  year = {1991},
  doi = {10.1002/cpa.3160440402},
  note = {\url{https://doi.org/10.1002/cpa.3160440402}}
}

@article{Gigli2011,
  author = {Nicola Gigli},
  title = {On {H}{\"o}lder continuity-in-time of the optimal transport map towards measures along a curve},
  journal = {Proceedings of the Edinburgh Mathematical Society},
  volume = {54},
  number = {2},
  pages = {401--409},
  year = {2011},
  doi = {10.1017/S001309150800117X},
  note = {\url{https://doi.org/10.1017/S001309150800117X}}
}

@article{Berman2021,
  author = {Robert J. Berman},
  title = {Convergence Rates for Discretized {Monge--Amp\`ere} Equations and Quantitative Stability of Optimal Transport},
  journal = {Foundations of Computational Mathematics},
  volume = {21},
  pages = {1099--1140},
  year = {2021},
  doi = {10.1007/s10208-020-09480-x},
  note = {\url{https://doi.org/10.1007/s10208-020-09480-x}}
}

@inproceedings{MerigotDelalandeChazal2020,
  author = {Quentin M{\'e}rigot and Alex Delalande and Fr{\'e}d{\'e}ric Chazal},
  title = {Quantitative stability of optimal transport maps and linearization of the {2-Wasserstein} space},
  booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics},
  series = {Proceedings of Machine Learning Research},
  volume = {108},
  pages = {3186--3196},
  publisher = {PMLR},
  year = {2020},
  note = {\url{https://proceedings.mlr.press/v108/merigot20a.html}}
}

@article{DelalandeMerigot2023,
  author = {Alex Delalande and Quentin M{\'e}rigot},
  title = {Quantitative stability of optimal transport maps under variations of the target measure},
  journal = {Duke Mathematical Journal},
  volume = {172},
  number = {17},
  pages = {3321--3357},
  year = {2023},
  doi = {10.1215/00127094-2022-0106},
  eprint = {2103.05934v2},
  archivePrefix = {arXiv},
  note = {\url{https://doi.org/10.1215/00127094-2022-0106}.
    Statement locators follow the author manuscript, version 2, 8 March 2023:
    \url{https://arxiv.org/abs/2103.05934v2}}
}

@article{Letrouit2026,
  author = {Cyril Letrouit},
  title = {Unstable optimal transport maps},
  journal = {Comptes Rendus. Math{\'e}matique},
  volume = {364},
  pages = {333--344},
  year = {2026},
  doi = {10.5802/crmath.834},
  note = {\url{https://doi.org/10.5802/crmath.834}}
}

@misc{LetrouitMerigot2024,
  author = {Cyril Letrouit and Quentin M{\'e}rigot},
  title = {Gluing methods for quantitative stability of optimal transport maps},
  howpublished = {arXiv:2411.04908v3},
  eprint = {2411.04908v3},
  archivePrefix = {arXiv},
  primaryClass = {math.AP},
  year = {2024},
  note = {First circulated 2024; cited version 3, 16 July 2026.
    To appear in Annales scientifiques de l'{\'E}cole normale sup{\'e}rieure.
    \url{https://arxiv.org/abs/2411.04908v3}}
}

@article{DivolNilesWeedPooladian2025,
  author = {Vincent Divol and Jonathan Niles-Weed and Aram-Alexandre Pooladian},
  title = {Tight stability bounds for entropic {Brenier} maps},
  journal = {International Mathematics Research Notices},
  volume = {2025},
  number = {7},
  pages = {rnaf078},
  year = {2025},
  doi = {10.1093/imrn/rnaf078},
  eprint = {2404.02855v1},
  archivePrefix = {arXiv},
  note = {\url{https://doi.org/10.1093/imrn/rnaf078}.
    Statement locators follow the author manuscript, version 1, 3 April 2024:
    \url{https://arxiv.org/abs/2404.02855v1}}
}

@misc{Merigot2026,
  author = {Quentin M{\'e}rigot},
  title = {Sharp stability of {Brenier} maps via quantitative regularity of potentials},
  howpublished = {HAL preprint hal-05616391},
  year = {2026},
  note = {\url{https://hal.science/hal-05616391}}
}

@misc{HanZhu2026,
  author = {Bang-Xian Han and Zhuo-Nan Zhu},
  title = {Two-mode stability for multi-marginal optimal transport maps},
  howpublished = {arXiv:2606.23037v1},
  eprint = {2606.23037v1},
  archivePrefix = {arXiv},
  primaryClass = {math.MG},
  year = {2026},
  note = {\url{https://arxiv.org/abs/2606.23037v1}}
}

@misc{CazellesPauwelsPortales2026,
  author = {Elsa Cazelles and Edouard Pauwels and L{\'e}o Portales},
  title = {Statistical Estimation of {Monge} Transport Maps via {Brenier} Potentials},
  howpublished = {arXiv:2604.22366v2},
  eprint = {2604.22366v2},
  archivePrefix = {arXiv},
  primaryClass = {math.OC},
  year = {2026},
  note = {Version 2, 2 September 2026.
    \url{https://arxiv.org/abs/2604.22366v2}}
}

@misc{ChewiEichingerPooladian2026,
  author = {Sinho Chewi and Katharina Eichinger and Aram-Alexandre Pooladian},
  title = {Near-{Lipschitz} stability of the {Kim--Milman} flow map},
  howpublished = {\href{https://arxiv.org/abs/2606.23383v1}{arXiv:2606.23383v1}},
  eprint = {2606.23383v1},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  year = {2026}
}

@misc{CajaLopezDelgadinoKitagawa2026,
  author = {F.-U. Caja-Lopez and Matias G. Delgadino and Jun Kitagawa},
  title = {Stability of optimal transport maps and second variation of the {2-Monge--Kantorovich} distance},
  howpublished = {\href{https://arxiv.org/abs/2605.24232v1}{arXiv:2605.24232v1}},
  eprint = {2605.24232v1},
  archivePrefix = {arXiv},
  primaryClass = {math.AP},
  year = {2026}
}

@article{Knothe1957,
  author = {Herbert Knothe},
  title = {Contributions to the theory of convex bodies},
  journal = {Michigan Mathematical Journal},
  volume = {4},
  number = {1},
  pages = {39--52},
  year = {1957},
  doi = {10.1307/mmj/1028990175},
  note = {\url{https://doi.org/10.1307/mmj/1028990175}}
}

@article{McCann1997,
  author = {Robert J. McCann},
  title = {A convexity principle for interacting gases},
  journal = {Advances in Mathematics},
  volume = {128},
  number = {1},
  pages = {153--179},
  year = {1997},
  doi = {10.1006/aima.1997.1634},
  note = {\url{https://doi.org/10.1006/aima.1997.1634}.
    \href{https://www.math.toronto.edu/mccann/papers/advances.pdf}{Published text}}
}

@article{KitagawaMerigotThibert2019,
  author = {Jun Kitagawa and Quentin M{\'e}rigot and Boris Thibert},
  title = {Convergence of a {Newton} algorithm for semi-discrete optimal transport},
  journal = {Journal of the European Mathematical Society},
  volume = {21},
  number = {9},
  pages = {2603--2651},
  year = {2019},
  doi = {10.4171/JEMS/889},
  eprint = {1603.05579v2},
  archivePrefix = {arXiv},
  note = {\url{https://doi.org/10.4171/JEMS/889}.
    Statement locators follow the author manuscript, version 2, 7 March 2017:
    \url{https://arxiv.org/abs/1603.05579v2}}
}

@article{CarlierGalichonSantambrogio2010,
  author = {Guillaume Carlier and Alfred Galichon and Filippo Santambrogio},
  title = {From {Knothe}'s transport to {Brenier}'s map and a continuation method for optimal transport},
  journal = {SIAM Journal on Mathematical Analysis},
  volume = {41},
  number = {6},
  pages = {2554--2576},
  year = {2010},
  doi = {10.1137/080740647},
  note = {\url{https://doi.org/10.1137/080740647}.
    \href{https://www.ceremade.dauphine.fr/~carlier/Knothe-Brenier-final.pdf}{Accepted author manuscript},
    4 November 2009}
}