The isometric embedding of the augmented Teichmüller space of a Riemann surface into the augmented Teichmüller space of its covering surface

Abstract

It is known that every finitely unbranched holomorphic covering π : → S of a compact Riemann surface S with genus g ≥ 2 induces an isometric embedding Φ_π : Teich(S) → Teich(). By the mutual relations between Strebel rays in Teich(S) and their embeddings in Teich(), we show that the augmented Teichmüller space can be isometrically embedded in the augmented Teichmüller space .