# Hyperbolic spaces in Teichmüller spaces

Christopher J. Leininger; Saul Schleimer

Journal of the European Mathematical Society (2014)

- Volume: 016, Issue: 12, page 2669-2692
- ISSN: 1435-9855

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topLeininger, Christopher J., and Schleimer, Saul. "Hyperbolic spaces in Teichmüller spaces." Journal of the European Mathematical Society 016.12 (2014): 2669-2692. <http://eudml.org/doc/277391>.

@article{Leininger2014,

abstract = {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 of $S$.},

author = {Leininger, Christopher J., Schleimer, Saul},

journal = {Journal of the European Mathematical Society},

keywords = {almost-isometric embedding; Teichmüller space; hyperbolic space; quadratic differential; complex of curves; Teichmüller space; almost-isometric embedding; hyperbolic space; quadratic differential; complex of curves},

language = {eng},

number = {12},

pages = {2669-2692},

publisher = {European Mathematical Society Publishing House},

title = {Hyperbolic spaces in Teichmüller spaces},

url = {http://eudml.org/doc/277391},

volume = {016},

year = {2014},

}

TY - JOUR

AU - Leininger, Christopher J.

AU - Schleimer, Saul

TI - Hyperbolic spaces in Teichmüller spaces

JO - Journal of the European Mathematical Society

PY - 2014

PB - European Mathematical Society Publishing House

VL - 016

IS - 12

SP - 2669

EP - 2692

AB - 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 of $S$.

LA - eng

KW - almost-isometric embedding; Teichmüller space; hyperbolic space; quadratic differential; complex of curves; Teichmüller space; almost-isometric embedding; hyperbolic space; quadratic differential; complex of curves

UR - http://eudml.org/doc/277391

ER -

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