Hyperbolic spaces in Teichmüller spaces

Abstract

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

22 pages, revised to reflect referee's comments