The verification of an inequality
In a recent paper [\textit{R. W. Barnard, L. Cole, K. Pearce} and \textit{G. Brock Williams}, Proc. Lond. Math. Soc. (3) 93, No. 2, 395--417 (2006; Zbl 1103.30012)], the authors verified a conjecture of Mejia and Pommerenke that the extremal value for the Schwarzian derivative of a hyperbolically convex function is realized by a symmetric hyperbolic ``strip'' mapping. In the proof appeared an assertion that ``using an extensive computational argument which considers several cases'', the problem of computing the Schwarzian derivative for hyperbolic polygons bounded by exactly two symmetric hyperbolic geodesics could be reduced to computing the Schwarzian derivative for hyperbolic polygons bounded by exactly two symmetric hyperbolic geodesics, under the assumption that the argument \(z\) of the Schwarzian derivative satisfies the restriction \(0 \leq z < 1\). In the present paper, the authors provide a verification for that assertion.
scientific article; zbMATH DE number 5635037