  Let $\Gamma$ be the fundamental group of a compact n-dimensional riemannian
manifold X of sectional curvature bounded above by -1. We suppose that $\Gamma$
is a free product of its subgroup A and B over the amalgamated subgroup C. We
prove that the critical exponent $\delta(C)$ of C satisfies $\delta(C) \geq
n-2$. The equality happens if and only if there exist an embedded compact
hypersurface Y in X, totally geodesic, of constant sectional curvature -1, with
fundamental group C and which separates X in two connected components whose
fundamental groups are A and B. Similar results hold if $\Gamma$ is an HNN
extension, or more generally if $\Gamma$ acts on a simplicial tree without
fixed point.
