Uniform growth of groups acting on Cartan-Hadamard spaces
نویسنده
چکیده
We say that Γ has uniform exponential growth if Ent Γ > 0. In [11], remarque 5.12, M. Gromov raised the question whether exponential growth always implies uniform exponential growth. The answer is negative, indeed, in [14] J.S. Wilson gave examples of finitely generated groups of exponential growth and non uniform exponential growth. Nevertheless, exponential growth implies uniform exponential growth for hyperbolic groups [12], geometrically finite groups of isometries of Hadamard manifolds with pinched negative curvature [1], solvable groups [13] and linear groups [10], [4], [3]. For further references see the exposition paper [7]. We suppose that (X, g) is a n-dimensional Cartan Hadamard manifold of pinched sectional curvature −a2 ≤ K ≤ −1. Our main result is the
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