The Teichmüller space of the ideal boundary (Q2504336)

For an open Riemann surface \(R\), one can consider various kinds of compactifications of \(R\). In this paper the author considers the Royden compactification \(R^*\) and the Kerékártó-Stoïlow compactification \(\widetilde{R}\). There is a natural projection \(\pi: R^*\to \widetilde R\) which is the identity on \(R\). \(dR=R^*-R\) is called the Royden boundary of \(R\). The essential boundary \(dR^0\) is the compact subset of \(dR\) which is not the part of the union of the inverse images by \(\pi\) of the punctures of \(R\). The author introduced the notion of ideal boundary on the essential boundary \(dR^0\) and then the concept of Teichmüller space for an ideal boundary. The main result is that such a Teichmüller space is a complex manifold.