THE GROWTH FUNCTION OF THE VOLUME OF GEODESIC BALLS IN RIEMANNIAN MANIFOLDS OF HYPERBOLIC TYPE

Abstract

Let (M, g) be a compact Riemannian manifold of hyperbolic type and X be its universal Riemannian covering. We study in this paper, the growth function of the geodesic balls of X. We show that the critical exponent of the group of deck transformations of X is equal to the volume entropy h g of M .