@misc{AlemanKouroupis2025,
  author = {Aleman, Alexandru and Kouroupis, Athanasios},
  title = {{Brennan}'s conjecture holds for semigroups of holomorphic functions},
  year = {2025},
  eprint = {2409.15074},
  archivePrefix = {arXiv},
  note = {Version 2, 14 April 2025; first posted 23 September 2024},
  doi = {10.48550/arXiv.2409.15074},
  url = {https://arxiv.org/abs/2409.15074v2}
}

@article{BeliaevSmirnov2010,
  author = {Beliaev, Dmitri and Smirnov, Stanislav},
  title = {Random conformal snowflakes},
  journal = {Annals of Mathematics},
  series = {Second Series},
  volume = {172},
  number = {1},
  pages = {597--615},
  year = {2010},
  doi = {10.4007/annals.2010.172.597},
  url = {https://annals.math.princeton.edu/2010/172-1/p12}
}

@article{Bertilsson1998,
  author = {Bertilsson, Daniel},
  title = {Coefficient estimates for negative powers of the derivative of univalent functions},
  journal = {Arkiv f{\"o}r Matematik},
  volume = {36},
  pages = {255--273},
  year = {1998},
  doi = {10.1007/BF02384769},
  url = {https://doi.org/10.1007/BF02384769}
}

@phdthesis{Bertilsson1999,
  author = {Bertilsson, Daniel},
  title = {On {Brennan}'s conjecture in conformal mapping},
  school = {Royal Institute of Technology},
  address = {Stockholm},
  year = {1999},
  url = {https://www.diva-portal.org/smash/get/diva2:8593/FULLTEXT01.pdf}
}

@article{Brennan1978,
  author = {Brennan, James E.},
  title = {The Integrability of the Derivative in Conformal Mapping},
  journal = {Journal of the London Mathematical Society (2)},
  volume = {18},
  number = {2},
  pages = {261--272},
  year = {1978},
  doi = {10.1112/jlms/s2-18.2.261},
  url = {https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms/s2-18.2.261}
}

@article{Brennan1978LOMI,
  author = {Brennan, James E.},
  title = {2.6. On the integrability of the derivative of conformal mapping},
  journal = {Zapiski Nauchnykh Seminarov LOMI},
  volume = {81},
  pages = {173--176},
  year = {1978},
  language = {Russian},
  url = {https://www.mathnet.ru/eng/znsl3048},
  note = {English translation: Journal of Soviet Mathematics 26(5) (1984), 2211--2213, doi:10.1007/BF01221542}
}

@article{CarlesonMakarov1994,
  author = {Carleson, Lennart and Makarov, Nikolai G.},
  title = {Some results connected with {Brennan}'s conjecture},
  journal = {Arkiv f{\"o}r Matematik},
  volume = {32},
  number = {1},
  pages = {33--62},
  year = {1994},
  doi = {10.1007/BF02559522},
  url = {https://doi.org/10.1007/BF02559522}
}

@book{Duren1983,
  author = {Duren, Peter L.},
  title = {Univalent Functions},
  series = {Grundlehren der mathematischen Wissenschaften},
  volume = {259},
  publisher = {Springer-Verlag},
  address = {New York},
  year = {1983},
  isbn = {978-0-387-90795-6},
  url = {https://link.springer.com/book/9780387907956}
}

@book{Folland1999,
  author = {Folland, Gerald B.},
  title = {Real Analysis: Modern Techniques and Their Applications},
  edition = {Second},
  publisher = {John Wiley \& Sons},
  address = {New York},
  year = {1999},
  isbn = {0-471-31716-0}
}

@article{GentnerLast2011,
  author = {Gentner, Daniel and Last, G{\"u}nter},
  title = {Palm pairs and the general mass-transport principle},
  journal = {Mathematische Zeitschrift},
  volume = {267},
  pages = {695--716},
  year = {2011},
  doi = {10.1007/s00209-009-0642-4},
  eprint = {0902.0068},
  archivePrefix = {arXiv},
  url = {https://link.springer.com/article/10.1007/s00209-009-0642-4}
}

@misc{GoldshteinUkhlov2013,
  author = {Gol'dshtein, Vladimir and Ukhlov, Alexander},
  title = {{Brennan}'s conjecture for composition operators on {Sobolev} spaces},
  howpublished = {arXiv:1212.3999v3},
  year = {2013},
  note = {Version 3, 14 February 2013; first posted 17 December 2012},
  doi = {10.48550/arXiv.1212.3999},
  url = {https://arxiv.org/abs/1212.3999v3}
}

@article{HedenmalmShimorin2005,
  author = {Hedenmalm, H{\aa}kan and Shimorin, Serguei},
  title = {Weighted {Bergman} spaces and the integral means spectrum of conformal mappings},
  journal = {Duke Mathematical Journal},
  volume = {127},
  number = {2},
  pages = {341--393},
  year = {2005},
  doi = {10.1215/S0012-7094-04-12725-3},
  eprint = {math/0406345},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1215/S0012-7094-04-12725-3}
}

@article{Hopf1935,
  author = {Hopf, Heinz},
  title = {{{\"U}ber die Drehung der Tangenten und Sehnen ebener Kurven}},
  journal = {Compositio Mathematica},
  volume = {2},
  pages = {50--62},
  year = {1935},
  url = {https://www.numdam.org/item/CM_1935__2__50_0/}
}

@misc{Jin2025IntegralMeans,
  author        = {Jin, Jianjun},
  title         = {Complex exponential integral means spectra of univalent functions and the {Brennan} conjecture},
  year          = {2025},
  eprint        = {2512.09330},
  archivePrefix = {arXiv},
  primaryClass  = {math.CV},
  note          = {Version 13, 5 June 2026; first posted 10 December 2025},
  doi           = {10.48550/arXiv.2512.09330},
  url           = {https://arxiv.org/abs/2512.09330v13}
}

@misc{Jin2026Multipliers,
  author        = {Jin, Jianjun},
  title         = {On the norms of the multiplication operators between weighted {Bergman} spaces},
  year          = {2026},
  eprint        = {2603.16170},
  archivePrefix = {arXiv},
  primaryClass  = {math.FA},
  note          = {Version 9, 16 May 2026},
  doi           = {10.48550/arXiv.2603.16170},
  url           = {https://arxiv.org/abs/2603.16170v9}
}

@book{Lee2013,
  author = {Lee, John M.},
  title = {Introduction to Smooth Manifolds},
  edition = {Second},
  series = {Graduate Texts in Mathematics},
  volume = {218},
  publisher = {Springer},
  address = {New York},
  year = {2013},
  doi = {10.1007/978-1-4419-9982-5},
  url = {https://doi.org/10.1007/978-1-4419-9982-5}
}

@book{Moschovakis2009,
  author = {Moschovakis, Yiannis N.},
  title = {Descriptive Set Theory},
  edition = {Second},
  series = {Mathematical Surveys and Monographs},
  volume = {155},
  publisher = {American Mathematical Society},
  address = {Providence, RI},
  year = {2009},
  doi = {10.1090/surv/155},
  isbn = {978-0-8218-4813-5},
  url = {https://www.ams.org/books/surv/155/}
}

@book{Munkres2014,
  author = {Munkres, James R.},
  title = {Topology},
  edition = {Second},
  note = {Pearson New International Edition},
  publisher = {Pearson Education},
  address = {Harlow},
  year = {2014},
  isbn = {978-1-292-02362-5}
}

@article{Pommerenke1985IntegralMeans,
  author = {Pommerenke, Christian},
  title = {On the Integral Means of the Derivative of a Univalent Function},
  journal = {Journal of the London Mathematical Society (2)},
  volume = {32},
  number = {2},
  pages = {254--258},
  year = {1985},
  doi = {10.1112/jlms/s2-32.2.254},
  url = {https://doi.org/10.1112/jlms/s2-32.2.254}
}

@article{Pommerenke1985IntegralMeansII,
  author = {Pommerenke, Christian},
  title = {On the Integral Means of the Derivative of a Univalent Function, {II}},
  journal = {Bulletin of the London Mathematical Society},
  volume = {17},
  number = {6},
  pages = {565--570},
  year = {1985},
  doi = {10.1112/blms/17.6.565},
  url = {https://doi.org/10.1112/blms/17.6.565}
}

@article{Sard1942,
  author = {Sard, Arthur},
  title = {The measure of the critical values of differentiable maps},
  journal = {Bulletin of the American Mathematical Society},
  volume = {48},
  pages = {883--890},
  year = {1942},
  doi = {10.1090/S0002-9904-1942-07811-6},
  url = {https://doi.org/10.1090/S0002-9904-1942-07811-6}
}

@article{Sola2006,
  author = {Sola, Alan},
  title = {An Estimate of the Universal Means Spectrum of Conformal Mappings},
  journal = {Computational Methods and Function Theory},
  volume = {6},
  number = {2},
  pages = {423--436},
  year = {2006},
  doi = {10.1007/BF03321620},
  url = {https://link.springer.com/article/10.1007/BF03321620}
}

@misc{Sola2007Thesis,
  author = {Sola, Alan},
  title = {{Bergman} space methods and integral means spectra of univalent functions},
  howpublished = {Licentiate thesis, Royal Institute of Technology, Stockholm},
  year = {2007},
  url = {https://www.diva-portal.org/smash/get/diva2:11935/FULLTEXT01.pdf}
}

@misc{Zheng2026Basins,
  author        = {Zheng, Yigang},
  title         = {{Brennan} Conjecture for Basin of Attraction at Infinity},
  year          = {2026},
  eprint        = {2604.12240},
  archivePrefix = {arXiv},
  primaryClass  = {math.DS},
  note          = {Version 1, 14 April 2026},
  doi           = {10.48550/arXiv.2604.12240},
  url           = {https://arxiv.org/abs/2604.12240v1}
}

@misc{OpenAIStrictInverseFirst2026,
  author = {{OpenAI}},
  title = {{A strict inverse-first-power bound for univalent functions}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/A-strict-inverse-first-power-bound-for-univalent-functions-September-24-2026/paper.pdf}{OAI:A-strict-inverse-first-power-bound-for-univalent-functions-September-24-2026}},
  year = {2026}
}