Let #GAMMA# be a geometrically finite discrete group of isometries of hyperbolic space H_F~n, where F = R, C, H or O (in which case n = 2). We prove that the critical exponent of #GAMMA# equals the Hausdorff dimension of the limit sets #LAMBDA#(#GAMMA#) and that the smallest eigenvalue of the Laplacian acting on square integrable functions is a quadratic function of either of them (when they are sufficiently large). A generalization of Hopf ergodicity theorem for the geodesic flow with respect to the Bowen-Margulis measure is also proven.
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