Geometric & Functional Analysis GAFA

, Volume 10, Issue 2, pp 266–306

Embeddings of Gromov hyperbolic spaces

  • M. Bonk
  • O. Schramm

DOI: 10.1007/s000390050009

Cite this article as:
Bonk, M. & Schramm, O. GAFA, Geom. funct. anal. (2000) 10: 266. doi:10.1007/s000390050009


It is shown that a Gromov hyperbolic geodesic metric space X with bounded growth at some scale is roughly quasi-isometric to a convex subset of hyperbolic space. If one is allowed to rescale the metric of X by some positive constant, then there is an embedding where distances are distorted by at most an additive constant.¶Another embedding theorem states that any \( \delta \)-hyperbolic metric space embeds isometrically into a complete geodesic \( \delta \)-hyperbolic space.¶The relation of a Gromov hyperbolic space to its boundary is further investigated. One of the applications is a characterization of the hyperbolic plane up to rough quasi-isometries.

Copyright information

© Birkhäuser Verlag, Basel 2000

Authors and Affiliations

  • M. Bonk
    • 1
  • O. Schramm
    • 2
  1. 1.Institut für Analysis, Technische Universität Braunschweig, D-38106 Braunschweig, Germany, e-mail: M.Bonk@tu-bs.deDE
  2. 2.Mathematics Department, The Weizmann Institute, Rehovot 76100, Israel, e-mail: