Hyperbolic spaces in Teichm\"uller spaces
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 Teichm\"uller 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.
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