Outradii of the Teichmüller spaces of Fuchsian groups of the second kind (Q1111728)

Under the Bers embedding, the Teichmüller space T(\(\Gamma)\) of a Fuchsian group \(\Gamma\) is embedded as bounded subset of a Banach space. The outradius 0(\(\Gamma)\) is \(\sup \| \phi \|\), \(\phi\in T(\Gamma)\). It is well-known that \(2<0(\Gamma)\leq 6\) and the authors have proved that \(0(\Gamma)<6\) if \(\Gamma\) is finitely-generated of the first kind [the first author, Tôhoku Math. J., II. Ser. 30, 607-612 (1978; Zbl 0398.30038)] and \(0(\Gamma)=6\) if \(\Gamma\) is finitely-generated of the second kind [the authors, J. Math. Kyoto Univ. 26, 3-30 (1986; Zbl 0603.30054)]. Here, they prove \(0(\Gamma)=6\) for all groups of the second kind, independent of the previous proof.