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

It is known that every finitely unbranched holomorphic covering pi:(S) over tilde -> S of a compact Riemann surface S with genus g >= 2 induces an isometric embedding phi(pi):Teich(S)-> Teich((S) over tilde). By the mutual relations between Strebel rays in Teich(S) and their embeddings in Teich((S) over tilde), we show that the 1st-strata space of the augmented Teichmuller space (Teich) over cap (S) can be embedded in the augmented Teichmuller space (Teich) over cap((S) over tilde) isometrically. Furthermore, we show that phi(pi) induces an isometric embedding from the set Teich(S) (B) (infinity) consisting of Busemann points in the horofunction boundary of Teich(S) into Teich((S) over tilde )B(infinity) with the detour metric.