Outradii of Teichmüller spaces of finitely generated Fuchsian groups of the second kind (Q1082489)

Under the Bers embedding, the Teichmüller space T(\(\Gamma)\) of a Fuchsian group \(\Gamma\) is a bounded domain in the Banach space \(B_ 2(\Gamma,\Delta^*)\). The outradius of \(\Gamma\), \(o(\Gamma)=\sup_{\phi \in T(\Gamma)}\| \phi \|\), and \(2<o(\Gamma)\leq 6\). Here the authors prove that for \(\Gamma\) finitely-generated of the second kind \(o(\Gamma)=6\). This strengthens results of \textit{T. Chu} [Discontin. Groups Riemann Surf., Proc. 1973 Conf. Univ. Maryland, 75-79 (1974; Zbl 0298.32012)] and contrasts with \(o(\Gamma)<6\) for \(\Gamma\) finitely- generated of the first kind [the first author, Tôhoku Math. J., II. Ser. 30, 607-612 (1978; Zbl 0398.30038)].