@article{FGR2014,
  author  = {Figalli, Alessio and Gallou{\"e}t, Thomas O. and Rifford, Ludovic},
  title   = {On the convexity of injectivity domains on nonfocal manifolds},
  journal = {SIAM Journal on Mathematical Analysis},
  volume  = {47},
  number  = {2},
  pages   = {969--1000},
  year    = {2015},
  doi     = {10.1137/140961821},
  note    = {\href{https://doi.org/10.1137/140961821}{doi:10.1137/140961821}.
             \href{https://gallouet.github.io/MTWCLNF.pdf}{Author's copy of the published article}.
             Theorem numbering refers to this published version}
}

@incollection{Figalli2010,
  author    = {Figalli, Alessio},
  title     = {Regularity of optimal transport maps [after {Ma--Trudinger--Wang} and {Loeper}]},
  booktitle = {S{\'e}minaire {Bourbaki}: volume 2008/2009, expos{\'e}s 997--1011},
  series    = {Ast{\'e}risque},
  number    = {332},
  pages     = {341--368},
  publisher = {Soci{\'e}t{\'e} math{\'e}matique de France},
  year      = {2010},
  note      = {Expos{\'e} no.~1009.
               \href{https://www.numdam.org/book-part/AST_2010__332__341_0/}{Numdam archive}}
}

@book{Hatcher2002,
  author    = {Hatcher, Allen},
  title     = {Algebraic Topology},
  publisher = {Cambridge University Press},
  year      = {2002},
  isbn      = {0-521-79540-0},
  note      = {\href{https://pi.math.cornell.edu/~hatcher/AT/AT.pdf}{Author's online edition},
               incorporating corrections for the 2015 reprinting}
}

@misc{Calegari2013,
  author       = {Calegari, Danny},
  title        = {Notes on {Riemannian} Geometry},
  howpublished = {Lecture notes, University of Chicago},
  year         = {2015},
  month        = apr,
  note         = {Dated April~1, 2015; based on a Spring 2013 course.
                  \href{https://math.uchicago.edu/~dannyc/courses/riem_geo_2013/riem_geo_notes.pdf}{Author's PDF}}
}

@article{MTW2005,
  author = {Ma, Xi-Nan and Trudinger, Neil S. and Wang, Xu-Jia},
  title = {Regularity of potential functions of the optimal transportation problem},
  journal = {Archive for Rational Mechanics and Analysis},
  volume = {177},
  number = {2},
  year = {2005},
  pages = {151--183},
  doi = {10.1007/s00205-005-0362-9},
  note = {\href{https://doi.org/10.1007/s00205-005-0362-9}{doi:10.1007/s00205-005-0362-9}}
}

@article{Loeper2009,
  author = {Loeper, Gr{\'e}goire},
  title = {On the regularity of solutions of optimal transportation problems},
  journal = {Acta Mathematica},
  volume = {202},
  number = {2},
  year = {2009},
  pages = {241--283},
  doi = {10.1007/s11511-009-0037-8},
  note = {\href{https://doi.org/10.1007/s11511-009-0037-8}{doi:10.1007/s11511-009-0037-8}}
}

@article{FRV2011,
  author = {Figalli, Alessio and Rifford, Ludovic and Villani, C{\'e}dric},
  title = {Necessary and sufficient conditions for continuity of optimal transport maps on {Riemannian} manifolds},
  journal = {Tohoku Mathematical Journal, Second Series},
  volume = {63},
  number = {4},
  year = {2011},
  pages = {855--876},
  doi = {10.2748/tmj/1325886291},
  note = {\href{https://doi.org/10.2748/tmj/1325886291}{doi:10.2748/tmj/1325886291}}
}

@article{LoeperVillani2010,
  author = {Loeper, Gr{\'e}goire and Villani, C{\'e}dric},
  title = {Regularity of optimal transport in curved geometry: the nonfocal case},
  journal = {Duke Mathematical Journal},
  volume = {151},
  number = {3},
  year = {2010},
  pages = {431--485},
  doi = {10.1215/00127094-2010-003},
  note = {\href{https://doi.org/10.1215/00127094-2010-003}{doi:10.1215/00127094-2010-003}}
}

@article{KM2010,
  author = {Kim, Young-Heon and McCann, Robert J.},
  title = {Continuity, curvature, and the general covariance of optimal transportation},
  journal = {Journal of the European Mathematical Society},
  volume = {12},
  number = {4},
  year = {2010},
  pages = {1009--1040},
  doi = {10.4171/JEMS/221},
  note = {\href{https://doi.org/10.4171/JEMS/221}{doi:10.4171/JEMS/221}}
}

@article{Moreau1965,
  author = {Moreau, Jean-Jacques},
  title = {Proximit{\'e} et dualit{\'e} dans un espace hilbertien},
  journal = {Bulletin de la Soci{\'e}t{\'e} Math{\'e}matique de France},
  volume = {93},
  year = {1965},
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  doi = {10.24033/bsmf.1625},
  note = {\href{https://doi.org/10.24033/bsmf.1625}{doi:10.24033/bsmf.1625}}
}

@article{MPW2012,
  author = {McCann, Robert J. and Pass, Brendan and Warren, Micah},
  title = {Rectifiability of optimal transportation plans},
  journal = {Canadian Journal of Mathematics},
  volume = {64},
  year = {2012},
  pages = {924--934},
  doi = {10.4153/CJM-2011-080-6},
  note = {\href{https://doi.org/10.4153/CJM-2011-080-6}{doi:10.4153/CJM-2011-080-6}.
          \href{https://arxiv.org/abs/1003.4556v1}{arXiv:1003.4556v1}}
}

@misc{Simon2018,
  author = {Simon, Leon},
  title = {Introduction to Geometric Measure Theory},
  howpublished = {NTU lecture notes},
  year = {2018},
  note = {Updated 7 March 2018; copyright 2017, 2018.
          \href{https://math.stanford.edu/~lms/ntu-gmt-text.pdf}{Author's PDF}}
}

@misc{Gorodski2016,
  author = {Gorodski, Claudio},
  title = {Variational calculus},
  howpublished = {Chapter 5 of {An introduction to Riemannian geometry}, MAT5771 course notes, IME-USP},
  year = {2016},
  note = {Revised chapter dated 8 June 2016 on the course page;
          PDF retains copyright 2012.
          \href{https://www.ime.usp.br/~gorodski/teaching/mat5771-2016/ch5.pdf}{Author's revised chapter}}
}

@article{Villani2011,
  author  = {Villani, C{\'e}dric},
  title   = {Regularity of optimal transport and cut locus: From nonsmooth analysis to geometry to smooth analysis},
  journal = {Discrete and Continuous Dynamical Systems},
  volume  = {30},
  number  = {2},
  pages   = {559--571},
  year    = {2011},
  doi     = {10.3934/dcds.2011.30.559},
  note    = {\href{https://doi.org/10.3934/dcds.2011.30.559}{doi:10.3934/dcds.2011.30.559}}
}

@article{TW2009,
  author  = {Trudinger, Neil S. and Wang, Xu-Jia},
  title   = {On the second boundary value problem for {Monge--Amp\`ere} type equations and optimal transportation},
  journal = {Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Serie V},
  volume  = {8},
  number  = {1},
  pages   = {143--174},
  year    = {2009},
  doi     = {10.2422/2036-2145.2009.1.07},
  note    = {\href{https://doi.org/10.2422/2036-2145.2009.1.07}{doi:10.2422/2036-2145.2009.1.07}.
             \href{https://arxiv.org/abs/math/0601086v4}{Author's preprint, version 4}}
}

@article{CMS2001,
  author  = {Cordero-Erausquin, Dario and McCann, Robert J. and Schmuckenschl{\"a}ger, Michael},
  title   = {A {Riemannian} interpolation inequality {\`a} la {Borell}, {Brascamp} and {Lieb}},
  journal = {Inventiones Mathematicae},
  volume  = {146},
  pages   = {219--257},
  year    = {2001},
  doi     = {10.1007/s002220100160},
  note    = {\href{https://doi.org/10.1007/s002220100160}{doi:10.1007/s002220100160}.
             \href{https://webusers.imj-prg.fr/~dario.cordero/Docs/articles/CMSinvent.pdf}{Author's copy of the published article}}
}

@article{AA1999,
  author  = {Alberti, Giovanni and Ambrosio, Luigi},
  title   = {A geometrical approach to monotone functions in {$\mathbb R^n$}},
  journal = {Mathematische Zeitschrift},
  volume  = {230},
  pages   = {259--316},
  year    = {1999},
  doi     = {10.1007/PL00004691},
  note    = {\href{https://doi.org/10.1007/PL00004691}{doi:10.1007/PL00004691}.
             \href{https://people.dm.unipi.it/alberti/ricerca/1997-99/monotone-rdc.pdf}{Author's manuscript}}
}