Hyperbolic spaces in Teichmüller spaces, with S. Schleimer.
 

abstract
 

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