A hypergeometric proof that 𝖨𝗌𝗈 is bijective

Bostan, Alin; Yurkevich, Sergey

doi:10.1090/proc/15836

A hypergeometric proof that $\mathsf {Iso}$ is bijective
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by Alin Bostan and Sergey Yurkevich PDF

Proc. Amer. Math. Soc. 150 (2022), 2131-2136 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.

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