In this paper we present a definition of Sobolev spaces with respect to general measures, prove some useful technical results, some of them generalizations of classical results with Lebesgue measureâ€¦ (More)

o. Introduction Throughout, mtd + l will be a fixed, complete, noncompact Riemannian manifold of constant negative sectional curvature and finite volume. Given a point p on mt, we denote by S(p) theâ€¦ (More)

By a tree T we mean a connected graph such that every subgraph obtained from T by removing any of its edges is not connected. In what follows we will only consider trees in which we distinguish aâ€¦ (More)

If X is a geodesic metric space and x1, x2, x3 âˆˆ X , a geodesic triangle T = {x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X . The space X is Î´-hyperbolic (in theâ€¦ (More)

ds = 2 jdzj 1 jzj2 : With this metric, S is a complete Riemannian manifold with constant curvature 1. The only Riemann surfaces which are left out are the sphere, the plane, the punctured plane andâ€¦ (More)

The study of hyperbolic graphs is an interesting topic since the hyperbolicity of a geodesic metric space is equivalent to the hyperbolicity of a graph related to it. The main result in this paper isâ€¦ (More)

In this paper we present a definition of Sobolev spaces with respect to general measures, prove some useful technical results, some of them generalizations of classical results with Lebesgue measureâ€¦ (More)

If X is a geodesic metric space and x1, x2, x3 âˆˆ X, a geodesic triangle T = {x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X. The space X is Î´-hyperbolic (in the Gromovâ€¦ (More)

We study in this paper estimates on the size of the sets of points which are well approximated by orbits of other points under certain dynamical systems. We apply the results obtained to theâ€¦ (More)