Hyperbolic groupoids: metric and measure

Hypergeometric Functions and Hyperbolic Metric

We obtain new inequalities for certain hypergeometric functions. Using these inequalities, we deduce estimates for the hyperbolic metric and the induced distance function on a certain canonical hyperbolic plane domain.

The Quasihyperbolic Metric and Associated Estimates on the Hyperbolic Metric

In this paper we investigate the geometry of the quasihyperbolic metric of domains in R". This metric arises from the conformally flat generalized Riemannian metric d(x, aD)' ldx I. Due to the fact that the density cl(x, aD) -t is not necessarily differentiable, the classical theories of Riemannian geometry do not apply to this metric. The quasihyperbolic metric has been found to have many inte...

Products of hyperbolic metric spaces

Uniform Domains and the Quasi-hyperbolic Metric

The hyperbolic metric and geometric function theory

The goal is to present an introduction to the hyperbolic metric and various forms of the Schwarz-Pick Lemma. As a consequence we obtain a number of results in geometric function theory.