THE ISOMETRIC EMBEDDING OF THE AUGMENTED TEICHMULLER SPACE OF A RIEMANN SURFACE INTO THE AUGMENTED TEICHMULLER SPACE OF ITS COVERING SURFACE

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 augmented Teichmuller space (Teich) over cap (S) can be isometrically embedded in the augmented Teichmuller space (Teich) over cap((S) over tilde).