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Geometriae Dedicata

, Volume 62, Issue 3, pp 281–298 | Cite as

Quasi-geodesic segments and Gromov hyperbolic spaces

  • Mario Bonk
Article

Abstract

It is known that for a geodesic metric space hyperbolicity in the sense of Gromov implies geodesic stability. In this paper it is shown that the converse is also true. So Gromov hyperbolicity and geodesic stability are equialent for geodesic metric spaces.

Mathematics Subject Classification (1991)

53C23 

Key words

Hyperbolicity stability quasi-geodesics 

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References

  1. [CDP]
    Coornaert, M., Delzant, T. and Papadopoulos, A.: Géométrie et théorie de groups, Les groupes hyperbolique de Gromov, Lecture Notes in Math. 1441, Springer, Berlin, Heidelberg, New York, 1990.Google Scholar
  2. [G-H]
    Ghys, E. and de la Harpe, P. (eds.): Sur les groupes hyperbolique d'après Mikhael Gromov, Birkhäuser, Boston, 1990.Google Scholar
  3. [Gro]
    Gromov, M.: Hyperbolic groups, in: Essays in Group Theory, S. M. Gersten (ed.), MSRI Publ. 8, Springer, Berlin, Heidelberg, New York, 1987, pp. 75–263.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Mario Bonk
    • 1
    • 2
  1. 1.Institut für AnalysisTechnische Universität BraunschweigBraunschweigGermany
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA

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