Annals of Global Analysis and Geometry

, Volume 31, Issue 1, pp 37–57 | Cite as

Asymptotic Geometry and Growth of Conjugacy Classes of Nonpositively Curved Manifolds

  • Gabriele LinkEmail author


Let X be a Hadamard manifold and Γ⊂Isom(X) a discrete group of isometries which contains an axial isometry without invariant flat half plane. We study the behavior of conformal densities on the limit set of Γ in order to derive a new asymptotic estimate for the growth rate of closed geodesics in not necessarily compact or finite volume manifolds.

Key words

Conjugacy classes closed geodesics conformal densities 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ballmann, W.: Axial isometries of manifolds of nonpositive curvature, Math. Ann. 259 (1982), 131–144.CrossRefMathSciNetGoogle Scholar
  2. 2.
    Ballmann, W.: Nonpositively curved manifolds of higher rank, Ann. of Math. 122 (1985), 597–609.CrossRefMathSciNetGoogle Scholar
  3. 3.
    Ballmann, W.: Lectures on Spaces of Nonpositive Curvature, DMV Seminar, Band 25, Birkhäuser, Basel, 1995.Google Scholar
  4. 4.
    Burns, K. and Spatzier, R.: Manifolds of nonpositive curvature and their buildings, Publ. Math. IHES 65 (1987), 35–59.MathSciNetGoogle Scholar
  5. 5.
    Coornaert, M. and Knieper, G.: Growth of conjugacy classes in Gromov hyperbolic spaces, Geom. Funct. Anal. 12 (2002), 464–478.CrossRefMathSciNetGoogle Scholar
  6. 6.
    Eberlein, P. and O'eill, B.: Visibility manifolds, Pacific J. Math. 46 (1973), 45–109.MathSciNetGoogle Scholar
  7. 7.
    Knieper, G.: Das Wachstum der Äquivalenzklassen geschlossener Geodätischer in kompakten Mannigfaltigkeiten, Arch. Math. 40 (1983), 559–568.CrossRefMathSciNetGoogle Scholar
  8. 8.
    Knieper, G.: On the asymptotic geometry of nonpositively curved manifolds, Geom. Funct. Anal. 7 (1997), 755–782.CrossRefMathSciNetGoogle Scholar
  9. 9.
    Knieper, G.: Hyperbolic dynamics and Riemannian geometry, Handbook of Dynamical Systems Vol. 1A, North-Holland, Amsterdam, 2002, 453–545.Google Scholar
  10. 10.
    Link, G.: Hausdorff dimension of limit sets of discrete subgroups of higher rank Lie groups, Geom. Funct. Anal. 14 (2004), 400–432.CrossRefMathSciNetGoogle Scholar
  11. 11.
    Margulis, G. A.: Applications of ergodic theory to the investigation of manifolds of negative curvature, Funkt. Anal. Appl. 3 (1969), 335–336.CrossRefMathSciNetGoogle Scholar
  12. 12.
    Margulis, G. A. and Sharp, R.: On Some Aspects of the Theory of Anosov Systems, Springer, Berlin, 2003.Google Scholar
  13. 13.
    Roblin, T.: Sur la fonction orbitale des groupes discrets en courbure négative, Ann. Inst. Fourier, Grenoble 52 (2002), 145–151.MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Mathematisches Institut IIUniversität KarlsruheKarlsruheGermany

Personalised recommendations