Isometric embeddings of subsets of boundaries of Teichmüller spaces of compact hyperbolic Riemann surfaces (Q2184638)

The paper studies the extension of an embedding between Teichmüller spaces to the respective boundaries. It is known that every finitely unbranched holomorphic covering \(\pi: \tilde{S} \rightarrow S\) of a compact Riemann surface \(S\) with genus \(g \geq 2\) induces an isometric embedding \(\Phi_{\pi} : \mathrm{Teich}(S) \rightarrow\mathrm{Teich}(\tilde{S})\). The authors show that the first strata space of the augmented Teichmüller space \(\widehat{\mathrm{Teich}(S)}\) can be embedded in the augmented Teichmüller space \(\widehat{\mathrm{Teich}(\tilde{S})}\) isometrically, by use of Strebel rays. Furthermore, the authors show that \(\Phi_{\pi}\) induces an isometric embedding from the set \(\mathrm{Teich}(S)_{B}(\infty)\) consisting of Busemann points in the horofunction boundary of \(\mathrm{Teich}(S)\) into \(\mathrm{Teich}(\tilde{S})_{B}(\infty)\) with the detour metric.