For figure methods, software, and visual-source credits, see Numerical references.
References are listed alphabetically by author surname, then by coauthors, year, and title. Follow a reference to the reading pages that use it. Citations within a page open its local reference list, with return links to the text.
Uwe Abresch and Joel Langer. The normalized curve shortening flow and homothetic solutions. Journal of Differential Geometry, 23(2):175–196, 1986. Original classification; the supplied survey and Complexity of parabolic systems were also consulted. URL: https://doi.org/10.4310/jdg/1214440025, doi:10.4310/jdg/1214440025.
Dylan J. Altschuler, Steven J. Altschuler, Sigurd B. Angenent, and Lani F. Wu. The zoo of solitons for curve shortening in ℝⁿ. Nonlinearity, 26(5):1189–1226, 2013. Citations use arXiv v1, July 17, 2012, 39 pages; Sections 1–8 reviewed for the curve-soliton expansion; downloaded PDF has a later typesetting date on its title page. URL: https://arxiv.org/abs/1207.4051v1, doi:10.1088/0951-7715/26/5/1189.
Henri Anciaux. Construction of Lagrangian Self-similar Solutions to the Mean Curvature Flow in $$\mathbb C^n$$. Geometriae Dedicata, 120:37–48, 2006. URL: https://doi.org/10.1007/s10711-006-9082-z, doi:10.1007/s10711-006-9082-z.
Sigurd Angenent, Tom Ilmanen, and David L. Chopp. A computed example of nonuniqueness of mean curvature flow in R3. Communications in Partial Differential Equations, 20(11–12):1937–1958, 1995. Supplied PDF has a publisher cover; article p. 1937 is PDF p. 2. Section 2 proves qualitative expander results; the genus-three shrinker is numerical Assertion 1 and the Main Result in Section 4 is conditional. URL: https://doi.org/10.1080/03605309508821158, doi:10.1080/03605309508821158.
Sigurd Angenent and Qian You. Ancient solutions to curve shortening with finite total curvature. 2018. arXiv:1803.01399v1. Selected theorem statements and construction passages checked November 6, 2026; proofs are cited, not independently verified. URL: https://arxiv.org/abs/1803.01399v1.
Sigurd B. Angenent. Shrinking doughnuts. In Nonlinear Diffusion Equations and Their Equilibrium States, 3, volume 7 of Progress in Nonlinear Differential Equations and Their Applications, pages 21–38. Birkhäuser, Boston, MA, 1992.
Sigurd B. Angenent and Juan J. L. Velázquez. Degenerate neckpinches in mean curvature flow. Journal für die reine und angewandte Mathematik, 482:15–66, 1997. Printed page = supplied PDF page + 14. Odd m at least 3 is the constructed family used here; asymptotic profiles are not exact time-dependent formulas. URL: https://doi.org/10.1515/crll.1997.482.15, doi:10.1515/crll.1997.482.15.
Shrey Aryan and Tang-Kai Lee. Non-uniqueness of geodesic limits and a question of grayson and gage. 2026. Reviewed arXiv edition 2608.04855v1. Theorem 1.1 and Theorem 5.1, Section 5 proof; exact omega-limit set, smooth reparametrized convergence and antipodally invariant nonround metrics. URL: https://arxiv.org/abs/2608.04855v1.
Pietro Baldi, Emanuele Haus, and Carlo Mantegazza. Existence of a lens-shaped cluster of surfaces self-shrinking by mean curvature. Mathematische Annalen, 375:1857–1881, 2019. URL: https://arxiv.org/abs/1811.07822, arXiv:1811.07822, doi:10.1007/s00208-019-01890-9.
Yakov Berchenko-Kogan. The entropy of the Angenent torus is approximately 1.85122. Experimental Mathematics, 30(4):587–594, 2021. Source locators refer to arXiv version 2, 5 August 2019, 14 pages; numerical estimates, not certified error bounds. URL: https://arxiv.org/abs/1808.08163v2, doi:10.1080/10586458.2019.1583616.
Jacob Bernstein and Lu Wang. A mountain-pass theorem for asymptotically conical self-expanders. 2020. arXiv:2003.13857v1. Selected theorem statements and construction passages checked November 6, 2026; proofs are cited, not independently verified. URL: https://arxiv.org/abs/2003.13857v1.
Jacob Bernstein and Lu Wang. Smooth compactness for spaces of asymptotically conical self-expanders of mean curvature flow. International Mathematics Research Notices, 2021(12):9016–9044, 2021. Chapter discussion uses the Introduction and Theorem 1.1 of arXiv v2. URL: https://arxiv.org/abs/1804.09076v2.
Jacob Bernstein and Lu Wang. The space of asymptotically conical self-expanders of mean curvature flow. Mathematische Annalen, 380:175–230, 2021. Chapter discussion uses the Introduction and Theorem 1.1 of arXiv v2. URL: https://arxiv.org/abs/1712.04366v2.
Jacob Bernstein and Lu Wang. A mountain-pass theorem for asymptotically conical self-expanders. Peking Mathematical Journal, 5(2):213–278, 2022. Chapter discussion uses the Introduction, Theorem 1.1, and Corollary 1.2 of arXiv v1. URL: https://arxiv.org/abs/2003.13857v1.
Jacob Bernstein and Lu Wang. Relative expander entropy in the presence of a two-sided obstacle and applications. Advances in Mathematics, 399:108284, 2022. Chapter discussion uses the Introduction, Theorem 1.1, and Remark 1.2 of arXiv v2. URL: https://arxiv.org/abs/1906.07863v2.
Jacob Bernstein and Lu Wang. Topological uniqueness for self-expanders of small entropy. Cambridge Journal of Mathematics, 10(4):785–833, 2022. Chapter discussion uses the Introduction and Theorem 1.1 of arXiv v2. URL: https://arxiv.org/abs/1902.02642v2.
Jacob Bernstein and Lu Wang. An integer degree for asymptotically conical self-expanders. Calculus of Variations and Partial Differential Equations, 62(7):200, 2023. Article 200; chapter discussion uses the Introduction and Theorem 1.1 of arXiv v1. URL: https://arxiv.org/abs/1807.06494v1.
Theodora Bourni, Nathan Burns, and Spencer Catron. Classification of Convex Ancient Solutions to Free Boundary Curve Shortening Flow in Convex Domains. The Journal of Geometric Analysis, 2025. URL: https://arxiv.org/abs/2404.08824, arXiv:2404.08824, doi:10.1007/s12220-025-02036-x.
Theodora Bourni and Giada Franz. Ancient solutions to free boundary mean curvature flow. arXiv preprint, 2026. URL: https://arxiv.org/abs/2602.08850, arXiv:2602.08850.
Theodora Bourni and Mat Langford. Classification of convex ancient free boundary curve shortening flows in the disc. Analysis & PDE, 16:2225–2240, 2023. URL: https://arxiv.org/abs/2111.06051, arXiv:2111.06051, doi:10.2140/apde.2023.16.2225.
Theodora Bourni and Mat Langford. Classification of convex ancient free boundary mean curvature flows in the ball. ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, pages 581–603, 2025. URL: https://arxiv.org/abs/2204.06710, arXiv:2204.06710, doi:10.2422/2036-2145.202206_007.
Theodora Bourni, Mat Langford, and Giuseppe Tinaglia. A collapsing ancient solution of mean curvature flow in $\mathbb R^3$. arXiv preprint, 2017. URL: https://arxiv.org/abs/1705.06981, arXiv:1705.06981.
Theodora Bourni, Mat Langford, and Giuseppe Tinaglia. The atomic structure of ancient grain boundaries. Geometry & Topology, 26:1849–1905, 2022. URL: https://arxiv.org/abs/2006.16338, arXiv:2006.16338, doi:10.2140/gt.2022.26.1849.
Theodora Bourni, Mathew Langford, and Alexander Mramor. On the construction of closed nonconvex nonsoliton ancient mean curvature flows. International Mathematics Research Notices, 2021:757–768, 2020. URL: https://arxiv.org/abs/1911.05641, arXiv:1911.05641, doi:10.1093/imrn/rnaa063.
Theodora Bourni and Alexander Mramor. Nonplanar ancient curve shortening flows in $\mathbb R^3$ from grim reapers. Mathematische Zeitschrift, 2023. URL: https://arxiv.org/abs/2201.02134, arXiv:2201.02134, doi:10.1007/s00209-023-03320-8.
Kahnrad Braxton, Tang-Kai Lee, and Jonathan J. Zhu. A stable self-shrinking mobius bundle in r4. 2026. Reviewed arXiv edition 2609.19648v1. Theorem 1.2; Section 2.1, quotient (2.2), metric and shrinker identity; Section 7.2 and Remarks 7.3–7.6, including exact entropy. No genericity theorem inferred. URL: https://arxiv.org/abs/2609.19648v1.
Simon Brendle. Embedded self-similar shrinkers of genus 0. Annals of Mathematics, 183:715–728, 2016. Chapter discussion cites Theorem 1 of arXiv v1, the compact genus-zero statement. URL: https://arxiv.org/abs/1411.4640v1.
Simon Brendle and Kyeongsu Choi. Uniqueness of convex ancient solutions to mean curvature flow in R3. Inventiones Mathematicae, 217:35–76, 2019. Supplied journal edition; Theorem 1.1 is on printed page 36, PDF page 2. URL: https://doi.org/10.1007/s00222-019-00859-4, doi:10.1007/s00222-019-00859-4.
Philip Broadbridge and Peter Vassiliou. The role of symmetry and separation in surface evolution and curve shortening. SIGMA, 7:052, 2011. 19 pages; published June 1, 2011. URL: https://www.emis.de/journals/SIGMA/2011/052/sigma11-052.pdf, doi:10.3842/SIGMA.2011.052.
Antonio Bueno. Translating solitons of the mean curvature flow in the space $\mathbb H^2\times \mathbb R$. Journal of Geometry, 2018. URL: https://arxiv.org/abs/1803.02783, arXiv:1803.02783, doi:10.1007/s00022-018-0447-x.
Antonio Bueno and Rafael López. A new family of translating solitons in hyperbolic space. arXiv preprint, 2024. URL: https://arxiv.org/abs/2402.05533, arXiv:2402.05533.
Antonio Bueno and Rafael López. The class of grim reapers in $\mathbb H^2\times \mathbb R$. arXiv preprint, 2024. URL: https://arxiv.org/abs/2402.05772, arXiv:2402.05772.
Reto Buzano, Huy The Nguyen, and Mario B. Schulz. Noncompact self-shrinkers for mean curvature flow with arbitrary genus. Journal für die reine und angewandte Mathematik, 818:35–52, 2025. Source locators refer to arXiv version 2, 5 September 2024, 18 pages. URL: https://arxiv.org/abs/2110.06027v2, doi:10.1515/crelle-2024-0073.
Ildefonso Castro and Ana M. Lerma. Translating solitons for Lagrangian mean curvature flow in complex Euclidean plane. International Journal of Mathematics, 23:1250101, 2012. URL: https://arxiv.org/abs/1007.1886, arXiv:1007.1886, doi:10.1142/s0129167x12501017.
Jui-En Chang. Stability of regular shrinkers in the network flow. The Journal of Geometric Analysis, 2026. URL: https://arxiv.org/abs/2107.04338, arXiv:2107.04338, doi:10.1007/s12220-026-02357-5.
Jui-En Chang and Yang-Kai Lue. Uniqueness of regular shrinkers with 2 closed regions. arXiv preprint, 2019. URL: https://arxiv.org/abs/1901.10315, arXiv:1901.10315.
Po-Yao Chang and Joel Spruck. Self-shrinkers to the mean curvature flow asymptotic to isoparametric cones. Transactions of the American Mathematical Society, 369:6565–6582, 2017. URL: https://arxiv.org/abs/1510.07183, arXiv:1510.07183, doi:10.1090/tran/6957.
Jingwen Chen, Tang-Kai Lee, Ao Sun, and Xinrui Zhao. Closed mean curvature flows with prescribed tangent flows. 2026. Citations refer to arXiv v1, July 26, 2026, 40 PDF pages. URL: https://arxiv.org/abs/2607.23879v1, arXiv:2607.23879.
Jingwen Chen and Ao Sun. Mean curvature flow with multiplicity 2 convergence in manifolds. Mathematische Annalen, 392(2):1943–1964, 2025. Source locators use arXiv v2, March 9, 2025, 19 pages; the arXiv abstract page adds the word closed to the title, whereas the PDF and published article use in manifolds. URL: https://arxiv.org/abs/2402.04521v2, doi:10.1007/s00208-025-03147-0.
Jingwen Chen and Ao Sun. Mean curvature flow with multiplicity 2 convergence in ℝ³. Analysis & PDE, 19:1029–1060, 2026. Source locators use arXiv v3, August 20, 2025, 30 pages, rather than the final journal pagination. URL: https://arxiv.org/abs/2312.17457v3, doi:10.2140/apde.2026.19.1029.
Letian Chen. On the Existence and Uniqueness of Ancient Rescaled Mean Curvature Flows. Communications in Analysis and Geometry, pages 1–45, 2026. URL: https://arxiv.org/abs/2212.10798, arXiv:2212.10798, doi:10.4310/cag.260928092010.
Xinfu Chen and Jong-Shenq Guo. Self-similar solutions of a 2-D multiple-phase curvature flow. Physica D, 229:22–34, 2007. URL: https://doi.org/10.1016/j.physd.2007.03.009, doi:10.1016/j.physd.2007.03.009.
Kyeongsu Choi, Jiuzhou Huang, and Taehun Lee. Ancient mean curvature flows with finite total curvature. Transactions of the American Mathematical Society, 2025. URL: https://arxiv.org/abs/2405.01062, arXiv:2405.01062, doi:10.1090/tran/9473.
Kyeongsu Choi, Dong-Hwi Seo, Wei-Bo Su, and Kai-Wei Zhao. Classification of ancient finite-entropy curve shortening flows. 2026. Reviewed edition 2603.09112v1; selected statements checked. URL: https://arxiv.org/abs/2603.09112v1.
David L. Chopp. Computing minimal surfaces via level set curvature flow. Journal of Computational Physics, 106(1):77–91, 1993. Fixed-boundary numerical minimal surfaces; the catenoid test is in Section 4.1, pp. 86–87. URL: https://doi.org/10.1006/jcph.1993.1092, doi:10.1006/jcph.1993.1092.
David L. Chopp. Computation of self-similar solutions for mean curvature flow. Experimental Mathematics, 3(1):1–15, 1994. Journal scan reviewed in full. Five numerical candidates in Sections 4.1–4.4 and 4.6; the four-handled dumbbell in Section 4.5 fails the self-similarity test. No existence proof is supplied. URL: https://doi.org/10.1080/10586458.1994.10504572, doi:10.1080/10586458.1994.10504572.
Adrian Chun-Pong Chu and Ao Sun. Genus one singularities in mean curvature flow. Geometry & Topology, 29(8):4299–4340, 2025. Source locators refer to arXiv version 3, 6 March 2025, 37 pages. URL: https://arxiv.org/abs/2308.05923v3, doi:10.2140/gt.2025.29.4299.
Julie Clutterbuck, Oliver C. Schnürer, and Felix Schulze. Stability of translating solutions to mean curvature flow. Calculus of Variations and Partial Differential Equations, 29(3):281–293, 2007. Citations use the author-hosted September 2005 manuscript, 12 pages. URL: https://www.math.uni-konstanz.de/~schnuere/fub/ocs019.pdf, doi:10.1007/s00526-006-0033-1.
Tobias H. Colding and William P. Minicozzi, II. Generic mean curvature flow I: generic singularities. Annals of Mathematics, 175(2):755–833, 2012. URL: https://doi.org/10.4007/annals.2012.175.2.7, doi:10.4007/annals.2012.175.2.7.
Tobias Holck Colding and William P. Minicozzi, II. Complexity of parabolic systems. Publications Mathématiques de l'IHÉS, 132:83–135, 2020. The supplied 53-page IHES PDF is used for source page locators. URL: https://www.numdam.org/articles/10.1007/s10240-020-00117-x/, doi:10.1007/s10240-020-00117-x.
Juan Dávila, Manuel del Pino, and Xuan Hien Nguyen. Finite topology self-translating surfaces for the mean curvature flow in R3. Advances in Mathematics, 320:674–729, 2017. Theorem 1.1, Figure 2, and Section 2 checked in the accepted manuscript for the bowl–catenoid and Scherk gluing illustrations. URL: https://arxiv.org/abs/1501.03867, doi:10.1016/j.aim.2017.09.014.
Juan Davila, Manuel del Pino, and Juncheng Wei. A Bernstein problem for translating solutions to the mean curvature flow. arXiv preprint, 2026. URL: https://arxiv.org/abs/2609.04675, arXiv:2609.04675.
R. F. de Lima, A. K. Ramos, and J. P. dos Santos. Solitons to Mean Curvature Flow in the hyperbolic 3-space. Revista Matemática Iberoamericana, 42:769–802, 2026. URL: https://arxiv.org/abs/2307.14136, arXiv:2307.14136, doi:10.4171/rmi/1593.
Ronaldo F. de Lima and Álvaro K. Ramos. Dynamical Stability of Translating Solitons to Mean Curvature Flow in Hyperbolic Space. arXiv preprint, 2026. URL: https://arxiv.org/abs/2602.02424, arXiv:2602.02424.
Ronaldo F. de Lima, Álvaro K. Ramos, and João Paulo dos Santos. Rotators-Translators to Mean Curvature Flow in $\mathbb H^2\times \mathbb R$. Archiv der Mathematik, 124:343–353, 2025. URL: https://arxiv.org/abs/2402.04757, arXiv:2402.04757, doi:10.1007/s00013-024-02076-9.
Qi Ding. Minimal cones and self-expanding solutions for mean curvature flows. Mathematische Annalen, 376:359–405, 2020. Citations use the supplied published 47-page PDF; printed page = PDF page + 358. URL: https://arxiv.org/abs/1503.02612, doi:10.1007/s00208-019-01941-1.
Gregory Drugan. An immersed $S^2$ self-shrinker. Transactions of the American Mathematical Society, 367(5):3139–3159, 2015. URL: https://arxiv.org/abs/1304.0032, doi:10.1090/S0002-9947-2014-06051-0.
Gregory Drugan and Stephen J. Kleene. Immersed self-shrinkers. Transactions of the American Mathematical Society, 369:7213–7250, 2017. URL: https://arxiv.org/abs/1306.2383, arXiv:1306.2383, doi:10.1090/tran/6907.
Gregory Drugan, Hojoo Lee, and Xuan Hien Nguyen. A survey of closed self-shrinkers with symmetry. Results in Mathematics, 73(1):32, 2018. Article 32, 32 pages; locators refer to the supplied published edition. URL: https://arxiv.org/abs/1708.09113, doi:10.1007/s00025-018-0763-3.
Gregory Drugan and Xuan Hien Nguyen. Shrinking doughnuts via variational methods. The Journal of Geometric Analysis, 28:3725–3746, 2018. Source locators refer to arXiv version 1, 29 August 2017, 18 pages. URL: https://arxiv.org/abs/1708.08808v1, doi:10.1007/s12220-017-9976-z.
Wenkui Du and Robert Haslhofer. On uniqueness and nonuniqueness of ancient ovals. arXiv preprint, 2021. URL: https://arxiv.org/abs/2105.13830, arXiv:2105.13830.
Klaus Ecker and Gerhard Huisken. Mean Curvature Evolution of Entire Graphs. The Annals of Mathematics, 130:453, 1989. URL: https://doi.org/10.2307/1971452, doi:10.2307/1971452.
Christopher G. Evans, Jason D. Lotay, and Felix Schulze. Remarks on the self-shrinking Clifford torus. 2020. Version 3, 10 June 2020; theorem and page locators refer to this supplied version. URL: https://arxiv.org/abs/1802.01423v3, arXiv:1802.01423.
Tomoki Fujii. Graphical translating solitons for the mean curvature flow and isoparametric functions. Tohoku Mathematical Journal, 76:391–410, 2024. URL: https://arxiv.org/abs/2109.14809, arXiv:2109.14809, doi:10.2748/tmj.20230112.
Tomoki Fujii and Naoyuki Koike. Translators invariant under hyperpolar actions. arXiv preprint, 2023. URL: https://arxiv.org/abs/2308.15790, arXiv:2308.15790.
Eddygledson Souza Gama, Francisco Martín, and Niels Martin Møller. Finite entropy translating solitons in slabs. 2025. arXiv:2209.01640v3. Selected theorem statements and construction passages checked November 6, 2026; proofs are cited, not independently verified. URL: https://arxiv.org/abs/2209.01640v3.
Höskuldur P. Halldórsson. Self-similar solutions to the curve shortening flow. Transactions of the American Mathematical Society, 364(10):5285–5309, 2012. URL: https://arxiv.org/abs/1007.1617v2, doi:10.1090/S0002-9947-2012-05632-7.
Höskuldur P. Halldórsson. Helicoidal surfaces rotating/translating under the mean curvature flow. Geometriae Dedicata, 162:45–65, 2013. URL: https://arxiv.org/abs/1106.4583v3, doi:10.1007/s10711-012-9716-2.
Robert Haslhofer and Or Hershkovits. Ancient solutions of the mean curvature flow. 2013. arXiv:1308.4095v1. Selected theorem statements and construction passages checked November 6, 2026; proofs are cited, not independently verified. URL: https://arxiv.org/abs/1308.4095v1.
David Hoffman, Tom Ilmanen, Francisco Martín, and Brian White. Graphical translators for mean curvature flow. 2018. Supplied 28-page preprint dated July 5, 2018. Catalogue locators refer to this edition. The inverted ratio in Theorem 2.4 is corrected using equation (1.4). URL: https://arxiv.org/abs/1805.10860v2.
David Hoffman, Tom Ilmanen, Francisco Martín, and Brian White. Notes on translating solitons for mean curvature flow. 2019. Supplied 20-page manuscript dated January 29, 2019; catalogue citations use its PDF page numbers, not the later published edition. URL: https://arxiv.org/abs/1901.09101.
David Hoffman, Francisco Martín, and Brian White. Scherk-like translators for mean curvature flow. 2020. Later detailed source for the constructions surveyed in the supplied 2019 notes. Theorems 2.3, 3.1, 6.1 and 11.1 and the infinite-entropy discussion checked in arXiv v4; proofs remain external to this catalogue. URL: https://arxiv.org/abs/1903.04617v4.
David Hoffman, Francisco Martín, and Brian White. Nguyen's tridents and the classification of semigraphical translators for mean curvature flow. 2022. Reviewed 26-page arXiv v2 edition, revised December 29, 2021, posted February 1, 2022. Theorem 1 and Figures 1–2, pages 1–3. Downward translation convention. URL: https://arxiv.org/abs/1909.09241v2.
David Hoffman, Francisco Martín, and Brian White. Translating annuli for mean curvature flow. 2024. arXiv:2308.02210v4. Selected theorem statements and construction passages checked November 6, 2026; proofs are cited, not independently verified. URL: https://arxiv.org/abs/2308.02210v4.
David Hoffman, Francisco Martín, and Brian White. Expanders for mean curvature flow and counterexamples to ilmanen's genus-reduction conjecture. 2026. arXiv:2605.09657v1. Selected theorem statements and construction passages checked November 6, 2026; proofs are cited, not independently verified. URL: https://arxiv.org/abs/2605.09657v1.
David Hoffman, Francisco Martín, and Brian White. Generating shrinkers by mean curvature flow. 2026. Checked arXiv version 3, January 21, 2026; manuscript revised January 20, 2026; 50 pages. URL: https://arxiv.org/abs/2502.20340v3, arXiv:2502.20340.
Gerhard Huisken and Carlo Sinestrari. Convex ancient solutions of the mean curvature flow. 2014. arXiv:1405.7509v1. Selected theorem statements and construction passages checked November 6, 2026; proofs are cited, not independently verified. URL: https://arxiv.org/abs/1405.7509v1.
Gerhard Huisken and Carlo Sinestrari. Convex ancient solutions of the mean curvature flow. Journal of Differential Geometry, 101(2):267–287, 2015. Chapter discussion uses the Introduction and Theorem 1.1 of arXiv v1. URL: https://arxiv.org/abs/1405.7509v1.
Tom Ilmanen, André Neves, and Felix Schulze. On short time existence for the planar network flow. Journal of Differential Geometry, 111(1):39–89, 2019. Citations use the published 51-page PDF; printed page = PDF page + 38. Source expander normalization is curvature vector = normal position, converted by dilation sqrt(2). URL: https://arxiv.org/abs/1407.4756, doi:10.4310/jdg/1547607687.
Tom Ilmanen and Brian White. Fattening in mean curvature flow. Ars Inveniendi Analytica, pages Paper No. 4, 32 pp., 2025. Checked arXiv version 3, April 4, 2025; theorem and page locators use this 32-page edition. URL: https://arxiv.org/abs/2406.18703v3, arXiv:2406.18703, doi:10.15781/cybg-mf32.
Yohsuke Imagi, Dominic Joyce, and Joana Oliveira dos Santos. Uniqueness results for special lagrangians and lagrangian mean curvature flow expanders in cm. 2016. Reviewed arXiv edition 1404.0271v2. Theorems 1.1–1.2, Remark 1.3, Examples 3.9 and 3.15; n ≥ 3, exactness, embeddedness and asymptotic rates retained. URL: https://arxiv.org/abs/1404.0271v2.
Dominic Joyce, Yng-Ing Lee, and Mao-Pei Tsui. Self-similar solutions and translating solitons for lagrangian mean curvature flow. 2010. Reviewed arXiv edition 0801.3721v2. Theorems A–F, Corollaries H–I, Sections 3–6. Periodic compact case E(a)(ii); plane-neck cases C–D; translator formula (18), with direct integral rewrite; constant-radius rotating subcase of G/H. URL: https://arxiv.org/abs/0801.3721v2.
Nikolaos Kapouleas, Stephen J. Kleene, and Niels Martin Møller. Mean curvature self-shrinkers of high genus: non-compact examples. Journal für die reine und angewandte Mathematik, 739:1–39, 2018. Source locators refer to arXiv version 3, 18 November 2014, 41 pages. URL: https://arxiv.org/abs/1106.5454v3, doi:10.1515/crelle-2015-0050.
Nikolaos Kapouleas and Peter McGrath. Generalizing the linearized doubling approach, I: general theory and new minimal surfaces and self-shrinkers. Cambridge Journal of Mathematics, 11(2):299–439, 2023. Source locators refer to arXiv version 4, 5 December 2022, 86 pages; published pagination was not independently inspected. URL: https://arxiv.org/abs/2001.04240v4, arXiv:2001.04240, doi:10.4310/CJM.2023.v11.n2.a1.
Daniel Ketover. Self-shrinking platonic solids. 2016. Source locators refer to arXiv version 1, 23 February 2016, 17 pages. Compactness is explicitly left unresolved. URL: https://arxiv.org/abs/1602.07271v1, arXiv:1602.07271, doi:10.48550/arXiv.1602.07271.
Daniel Ketover. Self-shrinkers whose asymptotic cones fatten. 2024. Version 2, 21 November 2024, 47 pages. URL: https://arxiv.org/abs/2407.01240v2, arXiv:2407.01240.
Stephen J. Kleene and Niels Martin Moller. Self-shrinkers with a rotational symmetry. Transactions of the American Mathematical Society, 366:3943–3963, 2014. URL: https://arxiv.org/abs/1008.1609, arXiv:1008.1609, doi:10.1090/S0002-9947-2014-05721-8.
Mat Langford, Yuxing Liu, and George McNamara. Ancient curve shortening flow in the disc with mixed boundary condition. Arnold Mathematical Journal, 011:93, 2025. URL: https://arxiv.org/abs/2404.01525, arXiv:2404.01525, doi:10.56994/armj.011.003.004.
Chen-Kuan Lee. Self-expanders to the mean curvature flow based on the generalized Lawson-Osserman cone. Geometriae Dedicata, 2023. URL: https://arxiv.org/abs/2211.05625, arXiv:2211.05625, doi:10.1007/s10711-023-00773-3.
Ping-Hung Lee and Chung-Jun Tsai. Infinite-time singularities with vanishing mean curvature for lagrangian mean curvature flow in gibbons–hawking spaces. 2026. Reviewed arXiv edition 2606.28767v1. Sections 2–3 for ambient metric and quotient PDE; Theorem 6.2 and its proof for precise initial slope/concavity hypotheses, N ≥ 3, vanishing H and log curvature / sqrt(t) bounds. URL: https://arxiv.org/abs/2606.28767v1.
Yng-Ing Lee and Mu-Tao Wang. Hamiltonian stationary shrinkers and expanders for lagrangian mean curvature flows. 2009. Reviewed arXiv edition 0707.0239v1. Section 2.2, equations for S and its metric; Proposition 2.2. Unit convention checked against the normalized Möbius map. URL: https://arxiv.org/abs/0707.0239v1.
Yng-Ing Lee and Mu-Tao Wang. Hamiltonian stationary cones and self-similar solutions in higher dimension. 2010. Reviewed edition 0802.0359v1; selected statements checked. URL: https://arxiv.org/abs/0802.0359v1.
Wei-Hung Liao. Self-Expanding Solutions to the Mean Curvature Flow for Multiphase Surfaces with Regular Junctions. arXiv preprint, 2025. URL: https://arxiv.org/abs/2512.02578, arXiv:2512.02578.
Xiaobo Liu and Chuu-Lian Terng. Ancient solutions to mean curvature flow for isoparametric submanifolds. Mathematische Annalen, 378:289–315, 2020. URL: https://arxiv.org/abs/1911.12535, arXiv:1911.12535, doi:10.1007/s00208-020-02055-9.
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