A hypergeometric proof that 𝖨𝗌𝗈 is bijective

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 ( I s o \mathsf {Iso} , to be proved bijective) as a quotient of Gaussian hypergeometric functions.