Quasi-metric and metric spaces

We give a short review of a construction of Frink to obtain a metric space from a quasi-metric space. By an example we illustrate the limits of the construction

A M\"obius Characterization of Metric Spheres

In this paper we characterize compact extended Ptolemy metric spaces with many circles up to M\"obius equivalence. This characterization yields a M\"obius characterization of the $n$-dimensional spheres $S^n$ and hemispheres $S^n_+$ when endowed with their chordal metrics. In particular, we show that every compact extended Ptolemy metric space with the property that every three points are contained in a circle is M\"obius equivalent to $(S^n,d_0)$ for some $n\ge 1$, the $n$-dimensional sphere $S^n$ with its chordal metric.Comment: 24 pages, 1 figur

Aperiodic colorings and tilings of Coxeter groups

We construct a limit aperiodic coloring of hyperbolic groups. Also we construct limit strongly aperiodic strictly balanced tilings of the Davis complex for all Coxeter groups

Products of hyperbolic metric spaces

Let (X_i,d_i), i=1,2, be proper geodesic hyperbolic metric spaces. We give a general construction for a ``hyperbolic product'' X_1{times}_h X_2 which is itself a proper geodesic hyperbolic metric space and examine its boundary at infinity.Comment: 17 page

Incidence axioms for the boundary at infinity of complex hyperbolic spaces

We characterize the boundary at infinity of a complex hyperbolic space as a compact Ptolemy space that satisfies four incidence axioms.Comment: 48 pages, 3 figure