Some properties of the slice regular Schwarzians (Q2075621)

For the slice regular Schwarzian defined in the theory of quaternionic slice regular functions by the author [Adv. Appl. Clifford Algebr. 29, No. 4, Paper No. 82, 10 p. (2019; Zbl 1427.30077)], the author shows properties similar to those for the well-known complex Schwarzian in the theory of functions of one complex variable. Included are estimates connecting local and global univalence and conditions to establish the quasiconformal extension to the sphere of some holomorphic functions. Also noted are analogues to the work of \textit{N. Steinmetz} [Ann. Acad. Sci. Fenn., Math. 39, No. 2, 503--511 (2014; Zbl 1302.30036)] connecting solutions of some differential equations defined from the complex Schwarzian with solutions of some Riccati equations.