Group actions on geodesic Ptolemy spaces (2008)
Foertsch, Thomas, Schroeder, Viktor
In this paper we study geodesic Ptolemy metric spaces $X$ which allow proper and cocompact isometric actions of crystallographic or, more generally, virtual polycyclic groups. We show that $X$ is...
Nonpositive Curvature and the Ptolemy Inequality (2007)
Foertsch, Thomas, Lytchak, Alexander, Schroeder, Viktor
We provide examples of nonlocally, compact, geodesic Ptolemy metric spaces which are not uniquely geodesic. On the other hand, we show that locally, compact, geodesic Ptolemy metric spaces are...
On 3-dimensional Asymptotically Harmonic Manifolds (2007)
Schroeder, Viktor, Shah, Hemangi
Let (M,g) be a complete, simply connected Riemannian manifold of dimension 3 without conjugate points. We show that M is a hyperbolic manifold of constant sectional curvature, provided M is...
Non-positive curvature and the Ptolemy inequality (2007)
Foertsch, Thomas, Lytchak, Alexander, Schroeder, Viktor
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 spaces are uniquely...
Erratum to: Nonpositive Curvature and the Ptolemy Inequality (2007)
Foertsch, Thomas, Lytchak, Alexander, Schroeder, Viktor
The following changes would like to be highlighted in the abstract: We provide examples of nonlocally compact, geodesic Ptolemy metric spaces that are not uniquely geodesic. On the other hand, we...
Aperiodic colorings and tilings of Coxeter groups (2006)
Dranishnikov, Alexander, Schroeder, Viktor
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.
Quasi-metric and metric spaces (2006)
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.
Hyperbolicity, CAT(-1)-spaces and the Ptolemy Inequality (2006)
Foertsch, Thomas, Schroeder, Viktor
Using a four points inequality for the boundary of CAT(-1)-spaces, we study the relation between Gromov hyperbolic spaces and CAT(-1)-spaces.
A product of trees as universal space for hyperbolic groups (2005)
Buyalo, Sergei, Schroeder, Viktor
We show that every Gromov hyperbolic group $\Ga$ admits a quasi-isometric embedding into the product of $(n+1)$ binary trees, where $n=\dim\di\Ga$ is the topological dimension of the boundary at...
Connecting geodesics and security of configurations in compact locally symmetric spaces (2005)
Gutkin, Eugene, Schroeder, Viktor
A pair of points in a riemannian manifold makes a secure configuration if the totality of geodesics connecting them can be blocked by a finite set. The manifold is secure if every configuration is...
Embedding of hyperbolic Coxeter groups into products of binary trees and aperiodic tilings (2005)
Dranishnikov, Alexander, Schroeder, Viktor
We prove that a finitely generated, right-angled, hyperbolic Coxeter group can be quasiisometrically embedded into the product of n binary trees, where n is the chromatic number of the group. As...
Affine functions on CAT(kappa) spaces (2004)
Lytschak, Alexander, Schroeder, Viktor
We study CAT(kappa) spaces X admitting affine functions. We show that there exists a canonical isometric embedding X -> Y x H where H is a Hilbert space, such that every affine function f: X -> R...
Embedding of Coxeter groups in a product of trees (2004)
Dranishnikov, Alexander, Schroeder, Viktor
We prove that a right angled Coxeter group with chromatic number n can be embedded in a bilipschitz way into the product of n locally finite trees. We give applications of this result to various...
Products of hyperbolic metric spaces II (2002)
Foertsch, Thomas, Schroeder, Viktor
In arXiv math.MG/0207296 we introduced a product construction for locally compact, complete, geodesic hyperbolic metric spaces. In the present paper we define the hyperbolic product for general...
Non Standard Metric Products (2002)
Bernig, Andreas, Foertsch, Thomas, Schroeder, Viktor
We consider a fairly general class of natural non standard metric products and classify those amongst them, which yield a product of certain type (for instance an inner metric space) for all possible...
Hyperbolic Rank of Products (2002)
Foertsch, Thomas, Schroeder, Viktor
Generalizing results due to Brady and Farb we prove the existence of a bilipschitz embedded manifold of pinched negative curvature and dimension m_1+m_2-1 in the product X:=X_1^{m_1} times X_2^{m_2}...
Products of hyperbolic metric spaces (2002)
Foertsch, Thomas, Schroeder, Viktor
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...
Minkowski- versus Euclidean rank for products of metric spaces (2001)
Foertsch, Thomas, Schroeder, Viktor
We introduce a notion of the Euclidean- and the Minkowski rank for arbitrary metric spaces and we study their behaviour with respect to products. We show that the Minkowski rank is additive with...
Hyperbolic rank and subexponential corank of metric spaces (2001)
Buyalo, Sergei, Schroeder, Viktor
We introduce a new quasi-isometry invariant $\subcorank X$ of a metric space $X$ called {\it subexponential corank}. A metric space $X$ has subexponential corank $k$ if roughly speaking there exists...
Über die Fundamentalgruppe von Räumen nichtpositiver Krümmung mit endlichem Volumen. (1983)
Münster (Westfalen), Univ., Diss., 1983 (Nicht f.d. Austausch).