977 research outputs found
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 -dimensional spheres and hemispheres
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 for some
, the -dimensional sphere 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
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