Hyperbolic spaces in Teichmüller spaces

  • Christopher J. Leininger

    University of Illinois at Urbana-Champaign, USA
  • Saul Schleimer

    University of Warwick, Coventry, United Kingdom


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

Cite this article

Christopher J. Leininger, Saul Schleimer, Hyperbolic spaces in Teichmüller spaces. J. Eur. Math. Soc. 16 (2014), no. 12, pp. 2669–2692

DOI 10.4171/JEMS/495