Isometric Embeddings of Subsets of Boundaries of Teichmüller Spaces of Compact Hyperbolic Riemann Surfaces

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 Φπ : Teich(S) → Teich(■).By the mutual relations between Strebel rays in Teich(S) and their embeddings in Teich(■), we show that the 1 st-strata space of the augmented Teichm¨ller space ■ can be embedded in the augmented Teichmüller space ■ isometrically. Furthermore, we show that Φπ induces an isometric embedding from the set Teich(S)B(∞) consisting of Busemann points in the horofunction boundary of Teich(S) into Teich(■)B(∞) with the detour metric.