Hyperbolic spaces in Teichmüller spaces
Hyperbolic spaces in Teichmüller spaces
We prove, for any n , that there is a closed connected orientable surface S so that the hyperbolic space \mathbb H^n almost-isometrically embeds into the Teichmüller space of S , with quasi-convex image lying in the thick part. As a consequence, \mathbb H^n quasi-isometrically embeds in the curve complex …