Kobayashi's and Teichmüller's metrics on the Teichmüller space of symmetric circle homeomorphisms (Q2430324)

In this short paper, the authors give a direct proof of the equality of the Kobayashi and Teichmüller metrics on the space of all symmetric orientation-preserving homeomorphisms of the unit circle modulo the space of all Möbius transformations preserving the unit circle, a result previously proved by \textit{C. J. Earle, F. P. Gardiner} and \textit{N. Lakic} [Contemporary Mathematics 355, 187--219 (2004; Zbl 1112.30034)] as a consequence of the general theory of Teichmüller spaces.