Uniform growth of groups acting on Cartan–Hadamard spaces

  • Gérard Besson

    Université Joseph Fourier, Grenoble, Saint-Martin-D'hères, France
  • Sylvestre Gallot

    Université Grenoble I, Saint-Martin-D'hères, France
  • Gilles Courtois

    Ecole Polytechnique, Palaiseau, France


In this paper we investigate the growth of finitely generated groups. We recall the definition of the algebraic entropy of a group and show that if the group is acting as a discrete subgroup of the isometry group of a Cartan–Hadamard manifold with pinched negative curvature then a Tits alternative is true. More precisely the group is either virtually nilpotent or has a uniform growth bounded below by an explicit constant.

Cite this article

Gérard Besson, Sylvestre Gallot, Gilles Courtois, Uniform growth of groups acting on Cartan–Hadamard spaces. J. Eur. Math. Soc. 13 (2011), no. 5, pp. 1343–1371

DOI 10.4171/JEMS/283