A hypergeometric proof that $\mathsf {Iso}$ is bijective
HTML articles powered by AMS MathViewer
- by Alin Bostan and Sergey Yurkevich
- Proc. Amer. Math. Soc. 150 (2022), 2131-2136
- DOI: https://doi.org/10.1090/proc/15836
- Published electronically: February 18, 2022
- PDF | Request permission
Abstract:
We provide a short and elementary proof of the main technical result of the recent article “Uniqueness of Clifford torus with prescribed isoperimetric ratio” by Thomas Yu and Jingmin Chen [Proc. Amer. Math. Soc. 150 (2022), pp. 1749–1765]. The key of the new proof is an explicit expression of the central function ($\mathsf {Iso}$, to be proved bijective) as a quotient of Gaussian hypergeometric functions.References
- George E. Andrews, Richard Askey, and Ranjan Roy, Special functions, Encyclopedia of Mathematics and its Applications, vol. 71, Cambridge University Press, Cambridge, 1999. MR 1688958, DOI 10.1017/CBO9781107325937
- Frédéric Chyzak, An extension of Zeilberger’s fast algorithm to general holonomic functions, Discrete Math. 217 (2000), no. 1-3, 115–134 (English, with English and French summaries). Formal power series and algebraic combinatorics (Vienna, 1997). MR 1766263, DOI 10.1016/S0012-365X(99)00259-9
- Stephen Melczer and Marc Mezzarobba, Sequence positivity through numeric analytic continuation: uniqueness of the Canham model for biomembranes, Technical Report, arXiv:2011.08155 [math.CO], 2020.
- Thomas Yu and Jingmin Chen, Uniqueness of Clifford torus with prescribed isoperimetric ratio, Proc. Amer. Math. Soc. 150 (2022), no. 4, 1749–1765. MR 4375762, DOI 10.1090/proc/15750
Bibliographic Information
- Alin Bostan
- Affiliation: Inria, Université Paris-Saclay, 1 rue Honoré d’Estienne d’Orves, 91120 Palaiseau, France
- MR Author ID: 725685
- ORCID: 0000-0003-3798-9281
- Email: alin.bostan@inria.fr
- Sergey Yurkevich
- Affiliation: Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria; and Inria, Université Paris-Saclay, 1 rue Honoré d’Estienne d’Orves, 91120 Palaiseau, France
- Email: sergey.yurkevich@univie.ac.at
- Received by editor(s): August 16, 2021
- Received by editor(s) in revised form: August 25, 2021, and September 1, 2021
- Published electronically: February 18, 2022
- Additional Notes: The first author was supported in part by DeRerumNatura ANR-19-CE40-0018. The second author was supported by Austrian Science Fund (FWF P-31338) and the DOC Fellowship of the Austrian Academy of Sciences (26101)
- Communicated by: Mourad Ismail
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 2131-2136
- MSC (2020): Primary 33C05
- DOI: https://doi.org/10.1090/proc/15836
- MathSciNet review: 4392347