Convexes hyperboliques et fonctions quasisymétriques

Yves Benoist

Publications Mathématiques de l'IHÉS (2003)

  • Volume: 97, page 181-237
  • ISSN: 0073-8301


Every bounded convex open set Ω of Rm is endowed with its Hilbert metric dΩ. We give a necessary and sufficient condition, called quasisymmetric convexity, for this metric space to be hyperbolic. As a corollary, when the boundary is real analytic, Ω is always hyperbolic. In dimension 2, this condition is: in affine coordinates, the boundary ∂Ω is locally the graph of a C1 strictly convex function whose derivative is quasisymmetric.

How to cite


Benoist, Yves. "Convexes hyperboliques et fonctions quasisymétriques." Publications Mathématiques de l'IHÉS 97 (2003): 181-237. <>.

author = {Benoist, Yves},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {hyperbolic convex sets; quasisymmetric functions},
language = {fre},
pages = {181-237},
publisher = {Springer},
title = {Convexes hyperboliques et fonctions quasisymétriques},
url = {},
volume = {97},
year = {2003},

AU - Benoist, Yves
TI - Convexes hyperboliques et fonctions quasisymétriques
JO - Publications Mathématiques de l'IHÉS
PY - 2003
PB - Springer
VL - 97
SP - 181
EP - 237
LA - fre
KW - hyperbolic convex sets; quasisymmetric functions
UR -
ER -


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