@misc{BK2024,
  author       = {Bamler, Richard H. and Kleiner, Bruce},
  title        = {On the multiplicity one conjecture for mean curvature flows of surfaces},
  year         = {2024},
  howpublished = {arXiv:2312.02106v3},
  eprint       = {2312.02106},
  archivePrefix = {arXiv},
  primaryClass = {math.DG},
  doi          = {10.48550/arXiv.2312.02106},
  url          = {https://arxiv.org/abs/2312.02106v3},
  note         = {Version 3, submitted 12 November 2024}
}

@misc{Wang2016,
  author       = {Wang, Lu},
  title        = {Asymptotic structure of self-shrinkers},
  year         = {2016},
  howpublished = {arXiv:1610.04904v1},
  eprint       = {1610.04904},
  archivePrefix = {arXiv},
  primaryClass = {math.DG},
  doi          = {10.48550/arXiv.1610.04904},
  url          = {https://arxiv.org/abs/1610.04904v1},
  note         = {Version 1, submitted 16 October 2016}
}

@article{Huisken1990,
  author       = {Huisken, Gerhard},
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  pages        = {285--299},
  doi          = {10.4310/jdg/1214444099},
  url          = {https://doi.org/10.4310/jdg/1214444099}
}

@article{White2005,
  author       = {White, Brian},
  title        = {A local regularity theorem for mean curvature flow},
  journal      = {Annals of Mathematics},
  volume       = {161},
  number       = {3},
  year         = {2005},
  pages        = {1487--1519},
  doi          = {10.4007/annals.2005.161.1487},
  url          = {https://annals.math.princeton.edu/2005/161-3/p07}
}

@article{INS2019,
  author       = {Ilmanen, Tom and Neves, Andr{\'e} and Schulze, Felix},
  title        = {On short time existence for the planar network flow},
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  volume       = {111},
  number       = {1},
  year         = {2019},
  pages        = {39--89},
  doi          = {10.4310/jdg/1547607687},
  eprint       = {1407.4756},
  archivePrefix = {arXiv},
  primaryClass = {math.AP},
  url          = {https://discovery.ucl.ac.uk/10064621/1/Schulze_Networkflow.pdf}
}

@article{CM2015,
  author       = {Colding, Tobias Holck and Minicozzi, II, William P.},
  title        = {Uniqueness of blowups and {{\L}ojasiewicz} inequalities},
  journal      = {Annals of Mathematics},
  volume       = {182},
  number       = {1},
  year         = {2015},
  pages        = {221--285},
  doi          = {10.4007/annals.2015.182.1.5},
  eprint       = {1312.4046},
  archivePrefix = {arXiv},
  primaryClass = {math.DG},
  url          = {https://annals.math.princeton.edu/2015/182-1/p05}
}

@article{Schulze2014,
  author       = {Schulze, Felix},
  title        = {Uniqueness of compact tangent flows in mean curvature flow},
  journal      = {Journal f{\"u}r die reine und angewandte Mathematik},
  volume       = {690},
  year         = {2014},
  pages        = {163--172},
  doi          = {10.1515/crelle-2012-0070},
  eprint       = {1107.4643},
  archivePrefix = {arXiv},
  primaryClass = {math.DG},
  url          = {https://arxiv.org/abs/1107.4643v3}
}

@article{CS2021,
  author       = {Chodosh, Otis and Schulze, Felix},
  title        = {Uniqueness of asymptotically conical tangent flows},
  journal      = {Duke Mathematical Journal},
  volume       = {170},
  number       = {16},
  year         = {2021},
  pages        = {3601--3657},
  doi          = {10.1215/00127094-2020-0098},
  eprint       = {1901.06369},
  archivePrefix = {arXiv},
  primaryClass = {math.DG},
  url          = {https://arxiv.org/abs/1901.06369v2}
}

@misc{Zhu2024,
  author       = {Zhu, Jonathan J.},
  title        = {{{\L}ojasiewicz} inequalities, uniqueness and rigidity for cylindrical self-shrinkers},
  year         = {2024},
  howpublished = {arXiv:2011.01633v2},
  eprint       = {2011.01633},
  archivePrefix = {arXiv},
  primaryClass = {math.DG},
  doi          = {10.48550/arXiv.2011.01633},
  url          = {https://arxiv.org/abs/2011.01633v2},
  note         = {Version 2, submitted 16 September 2024; first submitted 3 November 2020}
}

@article{AS2024,
  author       = {Aschenbrenner, Matthias and Srhir, Ahmed},
  title        = {Analytic {Nullstellens{\"a}tze} and the model theory of valued fields},
  journal      = {Mathematische Nachrichten},
  volume       = {297},
  number       = {8},
  year         = {2024},
  pages        = {2873--2917},
  doi          = {10.1002/mana.202200280},
  eprint       = {2207.03979},
  archivePrefix = {arXiv},
  url          = {https://www.mat.univie.ac.at/~maschenbrenner/pdf/Analytic%20Nullstellensatz.pdf},
  note         = {Corollary 4.8 in the March 2024 author version}
}

@article{Artin1968,
  author       = {Artin, M.},
  title        = {On the solutions of analytic equations},
  journal      = {Inventiones mathematicae},
  volume       = {5},
  year         = {1968},
  pages        = {277--291},
  doi          = {10.1007/BF01389777},
  url          = {https://doi.org/10.1007/BF01389777}
}

@article{Lojasiewicz1993,
  author       = {{\L}ojasiewicz, Stanislas},
  title        = {Sur la g{\'e}om{\'e}trie semi- et sous- analytique},
  journal      = {Annales de l'Institut Fourier},
  volume       = {43},
  number       = {5},
  year         = {1993},
  pages        = {1575--1595},
  doi          = {10.5802/aif.1384},
  url          = {https://www.numdam.org/articles/10.5802/aif.1384/}
}


@article{EckerHuisken1991,
  author  = {Ecker, Klaus and Huisken, Gerhard},
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  journal = {Inventiones mathematicae},
  volume  = {105},
  pages   = {547--569},
  year    = {1991},
  doi     = {10.1007/BF01232278},
  url     = {https://link.springer.com/article/10.1007/BF01232278}
}

@misc{Ilmanen1995,
  author = {Ilmanen, Tom},
  title = {Singularities of Mean Curvature Flow of Surfaces},
  year = {1995},
  eprint = {2601.21133},
  archivePrefix = {arXiv},
  primaryClass = {math.DG},
  doi = {10.48550/arXiv.2601.21133},
  url = {https://arxiv.org/abs/2601.21133v1},
  note = {Unpublished manuscript; archived in 2026 as arXiv:2601.21133v1}
}

@misc{Haslhofer2025,
  author = {Haslhofer, Robert},
  title = {Mean curvature flow through singularities},
  year = {2025},
  howpublished = {arXiv:2510.01355v1},
  eprint = {2510.01355},
  archivePrefix = {arXiv},
  primaryClass = {math.DG},
  doi = {10.48550/arXiv.2510.01355},
  url = {https://arxiv.org/abs/2510.01355v1},
  note = {Version 1; submitted to the Proceedings of the ICM 2026}
}

@article{CSS2007,
  author = {Clutterbuck, Julie and Schn{\"u}rer, Oliver C. and Schulze, Felix},
  title = {Stability of translating solutions to mean curvature flow},
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  volume = {29},
  year = {2007},
  pages = {281--293},
  doi = {10.1007/s00526-006-0033-1},
  eprint = {math/0509372},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/math/0509372v1}
}

@article{MR1992,
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}

@article{Costin1998,
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  eprint = {math/0608408},
  archivePrefix = {arXiv},
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@book{NP1994,
  author = {Nazarov, Sergey A. and Plamenevsky, Boris A.},
  title = {Elliptic Problems in Domains with Piecewise Smooth Boundaries},
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  publisher = {Walter de Gruyter},
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@book{Kato1995,
  author = {Kato, Tosio},
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  publisher = {Springer-Verlag},
  address = {Berlin and Heidelberg},
  year = {1995},
  note = {Reprint of the corrected 1980 edition},
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}

@book{Brakke1978,
  author = {Brakke, Kenneth A.},
  title = {The Motion of a Surface by Its Mean Curvature},
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  year = {1978}
}

@article{Simon1983,
  author = {Simon, Leon},
  title = {Asymptotics for a class of non-linear evolution equations, with applications to geometric problems},
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}

@article{BW2015,
  author = {Bernstein, Jacob and Wang, Lu},
  title = {A remark on a uniqueness property of high multiplicity tangent flows in dimension three},
  journal = {International Mathematics Research Notices},
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  number = {15},
  pages = {6286--6294},
  year = {2015},
  doi = {10.1093/imrn/rnu124},
  eprint = {1402.6687},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1402.6687v1}
}

@misc{Ghosh2026,
  author = {Ghosh, Sourav},
  title = {Cylindrical tangent flows in mean curvature flow},
  year = {2026},
  howpublished = {arXiv:2508.05517v3},
  eprint = {2508.05517},
  archivePrefix = {arXiv},
  primaryClass = {math.DG},
  doi = {10.48550/arXiv.2508.05517},
  url = {https://arxiv.org/abs/2508.05517v3},
  note = {Version 3, submitted 29 July 2026}
}

@misc{BamlerLai2026,
  author = {Bamler, Richard H. and Lai, Yi},
  title = {The {PDE-ODI} principle and cylindrical mean curvature flows},
  year = {2026},
  howpublished = {arXiv:2512.25050v2},
  eprint = {2512.25050},
  archivePrefix = {arXiv},
  doi = {10.48550/arXiv.2512.25050},
  url = {https://arxiv.org/abs/2512.25050v2},
  note = {Version 2, submitted 21 March 2026}
}

@article{AW1994,
  author = {Altschuler, Steven J. and Wu, Lang F.},
  title = {Translating surfaces of the non-parametric mean curvature flow with prescribed contact angle},
  journal = {Calculus of Variations and Partial Differential Equations},
  volume = {2},
  year = {1994},
  pages = {101--111},
  doi = {10.1007/BF01234317},
  url = {https://doi.org/10.1007/BF01234317}
}

@book{FS2009,
  author = {Flajolet, Philippe and Sedgewick, Robert},
  title = {Analytic Combinatorics},
  publisher = {Cambridge University Press},
  year = {2009},
  doi = {10.1017/CBO9780511801655},
  url = {https://doi.org/10.1017/CBO9780511801655}
}