Geodesic
Uniform growth of groups acting on Cartan–Hadamard spaces
Journal of the European Mathematical Society, Tome 13 (2011) no. 5, pp. 1343-1371.

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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.
DOI : 10.4171/jems/283
Classification : 20-XX, 00-XX 
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     author = {G\'erard Besson and Gilles Courtois and Sylvestre Gallot},
     title = {Uniform growth of groups acting on {Cartan{\textendash}Hadamard} spaces},
     journal = {Journal of the European Mathematical Society},
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Gérard Besson; Gilles Courtois; Sylvestre Gallot. Uniform growth of groups acting on Cartan–Hadamard spaces. Journal of the European Mathematical Society, Tome 13 (2011) no. 5, pp. 1343-1371. doi : 10.4171/jems/283. http://geodesic.mathdoc.fr/articles/10.4171/jems/283/

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