On shape of Teichmüller spaces (Q268043)

Let \(\Gamma\) be a Fuchsian group. The Teichmüller space \(T(\Gamma)\) has a holomorphic embedding, the Bers embedding, as a bounded domain formed by the Schwarzian derivates. The question is, whether the respective shape of \(T(\Gamma)\) is star-like. This question is not answered so far in general but if the dimension of \(T(\Gamma)\) is large enough then this shape is not star-like by M. Toki. Hence, especially, the universal Teichmüller space \(T(1)\) is not star-like. In this paper the author provides a much simpler geometric and constructive proof that \(T(1)\) is not star-like.