We introduce and discuss the concept of Gaussian probability density function (pdf) for the n-dimensional hyperbolic space which has been proposed as an environment for coding and decoding signals. An upper bound for the error probability of signal transmission associated with the hyperbolic distance is established. The pdf and the upper bound were developed using Poincaré models for the hyperb...

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.

Images are created using probabilistic iterated function systems that involve both affine transformations of the plane and isometries of hyperbolic geometry. Figures of attractors with striking hyperbolic symmetry are the result.

We study the volume growth function of geodesic spheres in the universal Riemann-ian covering of a compact manifold of hyperbolic type. Furthermore, we investigate the growth rate of closed geodesics in compact manifolds of hyperbolic type.