Products of Hyperbolic Metric Spaces

Products of hyperbolic metric spaces

Products of hyperbolic metric spaces II

In [FS] we introduced a product construction for locally compact, complete , geodesic hyperbolic metric spaces. In the present paper we define the hyperbolic product for general Gromov-hyperbolic spaces. In the case of roughly geodesic spaces we also analyse the boundary at infinity.

A product construction for hyperbolic metric spaces

Given two pointed Gromov hyperbolic metric spaces (Xi, di, zi), i = 1, 2, and ∆ ∈ R+0 , we present a construction method, which yields another Gromov hyperbolic metric space Y∆ = Y∆((X1, d1, z1), (X2, d2, z2)). Moreover, it is shown that once (Xi, di) is roughly geodesic, i = 1, 2, then there exists a ∆′ ≥ 0 such that Y∆ also is roughly geodesic for all ∆ ≥ ∆ ′.

Dimensions of Products of Hyperbolic Spaces

Estimates on asymptotic dimension are given for products of general hyperbolic spaces, with applications to hyperbolic groups. Examples are presented where strict inequality occurs in the product theorem for the asymptotic dimension in the class of hyperbolic groups and in the product theorem for the hyperbolic dimension. It is proved that R is dimensionally full for the asymptotic dimension in...

Characterizations of Metric Trees and Gromov Hyperbolic Spaces

A. In this note we give new characterizations of metric trees and Gromov hyperbolic spaces and generalize recent results of Chatterji and Niblo. Our results have a purely metric character, however, their proofs involve two classical tools from analysis: Stokes’ formula in R2 and a Rademacher type differentiation theorem for Lipschitz maps. This analytic approach can be used to give chara...