Metric characterizations of hyperbolic and Euclidean spaces

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...

On characterizations of hyperbolic harmonic Bloch and Besov spaces

‎We define hyperbolic harmonic $omega$-$alpha$-Bloch space‎ ‎$mathcal{B}_omega^alpha$ in the unit ball $mathbb{B}$ of ${mathbb R}^n$ and‎ ‎characterize it in terms of‎ ‎$$frac{omegabig((1-|x|^2)^{beta}(1-|y|^2)^{alpha-beta}big)|f(x)-f(y)|}{[x,y]^gamma|x-y|^{1-gamma}‎},$$ where $0leq gammaleq 1$‎. ‎Similar results are extended to‎ ‎little $omega$-$alpha$-Bloch and Besov spaces‎. ‎These obtained‎...

Products of hyperbolic metric spaces

Characterizations of Compactness for Metric Spaces

Characterizations of Sobolev Inequalities on Metric Spaces

We present isocapacitary characterizations of Sobolev inequalities in very general metric measure spaces.