@article{Dey1998,
 author={Dey, Tamal K.},
 title={Improved Bounds for Planar {$k$}-Sets and Related Problems},
 journal={Discrete \& Computational Geometry},
 volume={19}, number={3}, pages={373--382}, year={1998},
 doi={10.1007/PL00009354}, url={https://doi.org/10.1007/PL00009354}
}
@article{AgarwalAronovChanSharir1998,
 author={Agarwal, Pankaj K. and Aronov, Boris and Chan, Timothy M. and Sharir, Micha},
 title={On Levels in Arrangements of Lines, Segments, Planes, and Triangles},
 journal={Discrete \& Computational Geometry},
 volume={19}, pages={315--331}, year={1998},
 doi={10.1007/PL00009348},
 url={https://tmc.web.engr.illinois.edu/kset.pdf},
 note={Numbered and page locators refer to the author manuscript dated August 30, 1997}
}
@article{Toth2001,
 author={T{\'o}th, G{\'e}za},
 title={Point Sets with Many {$k$}-Sets},
 journal={Discrete \& Computational Geometry},
 volume={26}, number={2}, pages={187--194}, year={2001},
 doi={10.1007/s004540010022}, url={https://doi.org/10.1007/s004540010022}
}
@incollection{Nivasch2008,
 author={Nivasch, Gabriel},
 title={An Improved, Simple Construction of Many Halving Edges},
 booktitle={Surveys on Discrete and Computational Geometry: Twenty Years Later},
 series={Contemporary Mathematics}, volume={453}, pages={299--305},
 publisher={American Mathematical Society}, year={2008},
 doi={10.1090/conm/453/08804}, url={https://doi.org/10.1090/conm/453/08804}
}
@article{AlonsoLopezRodrigo2024,
 author={Alonso, Estrella and L{\'o}pez, Maril{\'o} and Rodrigo, Javier},
 title={An Improvement of the Upper Bound for the Number of Halving Lines of Planar Sets},
 journal={Symmetry}, volume={16}, number={7}, pages={936}, year={2024},
 doi={10.3390/sym16070936}, url={https://doi.org/10.3390/sym16070936}
}
@article{AjtaiEtAl1982,
 author={Ajtai, M. and Chv{\'a}tal, V. and Newborn, M. M. and Szemer{\'e}di, E.},
 title={Crossing-Free Subgraphs},
 journal={Annals of Discrete Mathematics}, volume={12}, pages={9--12}, year={1982},
 doi={10.1016/S0304-0208(08)73484-4}, url={https://doi.org/10.1016/S0304-0208(08)73484-4}
}
@book{Leighton1983,
 author={Leighton, Frank Thomson},
 title={Complexity Issues in {VLSI}: Optimal Layouts for the Shuffle-Exchange Graph and Other Networks},
 series={Foundations of Computing}, publisher={MIT Press}, year={1983},
 isbn={9780262121040}, url={https://mitpress.mit.edu/9780262121040/complexity-issues-in-vlsi/}
}
@article{ChabrillacCrouzeix1987,
 author={Chabrillac, Yves and Crouzeix, Jean-Pierre},
 title={Continuity and Differentiability Properties of Monotone Real Functions of Several Real Variables},
 journal={Mathematical Programming Study}, volume={30}, pages={1--16}, year={1987},
 doi={10.1007/BFb0121151}, url={https://doi.org/10.1007/BFb0121151}
}
@article{BorweinBurkeLewis2004,
 author={Borwein, Jonathan M. and Burke, James V. and Lewis, Adrian S.},
 title={Differentiability of Cone-Monotone Functions on Separable {Banach} Space},
 journal={Proceedings of the American Mathematical Society},
 volume={132}, number={4}, pages={1067--1076}, year={2004},
 doi={10.1090/S0002-9939-03-07149-1},
 url={https://sites.math.washington.edu/~burke/papers/reprints/46-cone-monotone.pdf}
}
@misc{VianaRokhlin,
 author={Viana, Marcelo},
 title={Disintegration into Conditional Measures: {Rokhlin}'s Theorem},
 year={n.d.}, note={Undated author lecture notes},
 url={https://w3.impa.br/~viana/out/rokhlin.pdf}
}

@article{Lovasz1971,
  author = {Lov{\'a}sz, L{\'a}szl{\'o}},
  title = {On the Number of Halving Lines},
  journal = {Annales Universitatis Scientiarum Budapestinensis de Rolando E{\"o}tv{\"o}s Nominatae, Sectio Mathematica},
  volume = {14},
  pages = {107--108},
  year = {1971}
}


@incollection{ErdosLovaszSimmonsStraus1973,
  author = {Erd{\H o}s, Paul and Lov{\'a}sz, L{\'a}szl{\'o} and Simmons, A. and Straus, Ernst G.},
  title = {Dissection Graphs of Planar Point Sets},
  booktitle = {A Survey of Combinatorial Theory},
  publisher = {North-Holland},
  address = {Amsterdam},
  pages = {139--149},
  year = {1973},
  url = {https://users.renyi.hu/~p_erdos/1973-07.pdf}
}


@article{PachSteigerSzemeredi1992,
  author = {Pach, J{\'a}nos and Steiger, William and Szemer{\'e}di, Endre},
  title = {An Upper Bound on the Number of Planar {$k$}-Sets},
  journal = {Discrete \& Computational Geometry},
  volume = {7},
  number = {2},
  pages = {109--123},
  year = {1992},
  doi = {10.1007/BF02187829},
  url = {https://doi.org/10.1007/BF02187829}
}


@inproceedings{Pinchasi2009,
  author = {Pinchasi, Rom},
  title = {Halving Lines and Measure Concentration in the Plane},
  booktitle = {Proceedings of the 25th Annual Symposium on Computational Geometry},
  series = {SCG '09},
  publisher = {Association for Computing Machinery},
  address = {New York, NY, USA},
  pages = {141--147},
  year = {2009},
  doi = {10.1145/1542362.1542393},
  url = {https://doi.org/10.1145/1542362.1542393}
}

@article{ArtsteinSlomka2017,
  author = {Artstein-Avidan, Shiri and Slomka, Boaz A.},
  title = {The Fundamental Theorems of Affine and Projective Geometry Revisited},
  journal = {Communications in Contemporary Mathematics},
  volume = {19},
  number = {5},
  pages = {1650059},
  year = {2017},
  doi = {10.1142/S0219199716500590},
  eprint = {1604.01762},
  archivePrefix = {arXiv},
  primaryClass = {math.GM},
  url = {https://doi.org/10.1142/S0219199716500590}
}


@article{PachSolymosiTardos2010,
  author = {Pach, J{\'a}nos and Solymosi, J{\'o}zsef and Tardos, G{\'a}bor},
  title = {Crossing Numbers of Imbalanced Graphs},
  journal = {Journal of Graph Theory},
  volume = {64},
  number = {1},
  pages = {12--21},
  year = {2010},
  doi = {10.1002/jgt.20435},
  url = {https://doi.org/10.1002/jgt.20435}
}

@article{Rademacher1919,
  author  = {Rademacher, Hans},
  title   = {{\"U}ber partielle und totale Differenzierbarkeit von Funktionen mehrerer Variabeln und {\"u}ber die Transformation der Doppelintegrale},
  journal = {Mathematische Annalen},
  volume  = {79},
  number  = {4},
  pages   = {340--359},
  year    = {1919},
  doi     = {10.1007/BF01498415},
  url     = {https://doi.org/10.1007/BF01498415}
}


@misc{Simon2014GMT,
  author       = {Simon, Leon},
  title        = {Introduction to Geometric Measure Theory},
  year         = {2014},
  howpublished = {Tsinghua lecture notes},
  note         = {2014 draft},
  url          = {https://web.stanford.edu/class/math285/ts-gmt.pdf}
}


@misc{PayneRedaelli2025preprint,
  author        = {Payne, Kevin R. and Redaelli, Davide Francesco},
  title         = {A Primer on Semiconvex Functions in General Potential Theories},
  year          = {2025},
  eprint        = {2303.14477},
  archivePrefix = {arXiv},
  primaryClass  = {math.AP},
  note          = {Version 3, 15 April 2025; Appendix B, Corollary B.4, p. 117},
  url           = {https://arxiv.org/abs/2303.14477v3}
}


@article{PascolettiZanolin2010,
  author = {Pascoletti, Anna and Zanolin, Fabio},
  title = {A Path Crossing Lemma and Applications to Nonlinear Second Order Equations under Slowly Varying Perturbations},
  journal = {Le Matematiche},
  volume = {65},
  number = {2},
  pages = {121--168},
  year = {2010},
  doi = {10.4418/2010.65.2.13},
  url = {https://doi.org/10.4418/2010.65.2.13}
}

@article{Siebenmann2005,
  author = {Siebenmann, L.},
  title = {The {Osgood--Schoenflies} Theorem Revisited},
  journal = {Russian Mathematical Surveys},
  volume = {60},
  number = {4},
  pages = {645--672},
  year = {2005},
  doi = {10.1070/RM2005v060n04ABEH003672},
  url = {https://doi.org/10.1070/RM2005v060n04ABEH003672}
}