We prove, for any , that there is a closed connected orientable surface so that the hyperbolic space almost-isometrically embeds into the Teichmüller space of , with quasi-convex image lying in the thick part. As a consequence, quasi-isometrically embeds in the curve complex of .
Cite this article
Christopher J. Leininger, Saul Schleimer, Hyperbolic spaces in Teichmüller spaces. J. Eur. Math. Soc. 16 (2014), no. 12, pp. 2669–2692DOI 10.4171/JEMS/495