We prove some finiteness results for discrete isometry groups Gamma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{ ...
The goal of this paper is to continue the study of the relation between the Poincar & eacute; inequality and the lower bounds of Minkowski content of separating sets, initiated in our previous work [5]. A new shorter proof is provided. It is based on the s ...
For a proper, Gromov-hyperbolic metric space and a discrete, non-elementary, group of isometries, we define a natural subset of the limit set at infinity of the group called the ergodic limit set. The name is motivated by the fact that every ergodic measur ...
We define the chain Sobolev space on a possibly non-complete metric measure space in terms of chain upper gradients. In this context, E-chains are finite collections of points with distance at most E between consecutive points. They play the role of discre ...
We study geometric characterizations of the Poincare inequality in doubling metric measure spaces in terms of properties of separating sets. Given a couple of points and a set separating them, such properties are formulated in terms of several possible not ...
We prove a quantitative version of the classical Tits' alternative for discrete groups acting on packed Gromov-hyperbolic spaces supporting a convex geodesic bicombing. Some geometric consequences, as uniform estimates on systole, diastole, algebraic entro ...
We prove that the Ahlfors regular conformal dimension is upper semicontinuous with respect to Gromov-Hausdorff convergence when restricted to the class of uniformly perfect, uniformly quasi-selfsimilar metric spaces. Moreover, we show the continuity of the ...