23 citations · 36 across the 14 of their papers we have counts for
14 papers
Hilbert space factor of metric spaces
Thomas Foertsch, Alexander Lytchak, Elefterios Soultanis
We prove that any complete metric space has a unique decomposition as a direct product of a possibly finite or zero-dimensional Hilbert space and a space that does not split off li…
A Möbius Characterization of Metric Spheres
Thomas Foertsch, Viktor Schroeder
In this paper we characterize compact extended Ptolemy metric spaces with many circles up to Möbius equivalence. This characterization yields a Möbius characterization of the -d…
Group actions on geodesic Ptolemy spaces
Thomas Foertsch, Viktor Schroeder
In this paper we study geodesic Ptolemy metric spaces which allow proper and cocompact isometric actions of crystallographic or, more generally, virtual polycyclic groups. We s…
Non-positive curvature and the Ptolemy inequality
Thomas Foertsch, Alexander Lytchak, Viktor Schroeder
We provide examples of non-locally compact geodesic Ptolemy metric spaces which are not uniquely geodesic. On the other hand, we show that locally compact, geodesic Ptolemy metric…
The de Rham decomposition theorem for metric spaces
Thomas Foertsch, Alexander Lytchak
We generalize the classical de Rham decomposition theorem for Riemannian manifolds to the setting of geodesic metric spaces of finite dimension.
Hyperbolicity, CAT(-1)-spaces and the Ptolemy Inequality
Thomas Foertsch, Viktor Schroeder
Using a four points inequality for the boundary of CAT(-1)-spaces, we study the relation between Gromov hyperbolic spaces and CAT(-1)-spaces.