On the growth of nonuniform lattices in pinched negatively curved manifolds

We study the relation between the exponential growth rate of volume in a pinched negatively curved manifold and the critical exponent of its lattices. These objects have a long and interesting story and are closely related to the geometry and the dynamical properties of the geodesic flow of the manifold

Volume growth and rigidity of negatively curved manifolds of finite volume

We study the asymptotic behaviour of the volume growth function of simply connected, Riemannian manifolds X of strictly negative curvature admitting a non-uniform lattice Γ. If X is asymptotically 1/4-pinched, we prove that Γ is divergent, with finite Bowen-Margulis measure, and that the volume growth of balls B(x, R) in X is asymptotically equivalent to a purely exponential function c(x)e ω(X)R , where ω(X) is the volume entropy of X. This generalizes Margulis' celebrated theorem for negatively curved spaces with compact quotients. A crucial step for this is a finite-volume version of the entropy-rigidity characterization of constant curvature spaces: any finite volume n-manifold with sectional curvature −b 2 ≤ k(X) ≤ −1 and volume entropy equal to (n − 1) is hyperbolic. In contrast, we show that for spaces admitting lattices which are not 1/4-pinched, depending on the critical exponent of the parabolic subgroups and on the finiteness of the Bowen-Margulis measure, the growth function can be exponential, lower-exponential or even upper-exponential

Adsorption of water molecules on oxidized graphite surfaces: A molecular dynamics study of the competition between OH and COOH sites

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