Poznámka o trojúhelnících racionálných
Products of simple isometries of given conjugacy types.
Proper holomorphic mappings and real reflection groups.
Proximinality in geodesic spaces.
Radical relations in unitary, symplectic, and orthogonal groups.
Ramsey partitions and proximity data structures
This paper addresses two problems lying at the intersection of geometric analysis and theoretical computer science: The non-linear isomorphic Dvoretzky theorem and the design of good approximate distance oracles for large distortion.We introduce the notion of Ramsey partitions of a finite metric space, and show that the existence of good Ramsey partitions implies a solution to the metric Ramsey problem for large distortion (also known as the non-linear version of the isomorphic Dvoretzky theorem,...
Reflection loops of spaces with congruence and hyperbolic incidence structure
In an absolute space with congruence there are line reflections and point reflections. With the help of point reflections one can define in a natural way an addition + of points which is only associative if the product of three point reflection is a point reflection again. In general, for example for the case that is a linear space with hyperbolic incidence structure, the addition is not associative. is a K-loop or a Bruck loop.
Relationen zwischen Symmetrien in orthogonalen Gruppen.
Relationen zwischen symplektischen Transvektionen.
Remark on "Planes with analogues to Eucledian angular bisectors".
Réseaux de Coxeter-Davis et commensurateurs
For each integer and each finite graph , we construct a Coxeter group and a non positively curved polygonal complex on which acts properly cocompactly, such that each polygon of has edges, and the link of each vertex of is isomorphic to . If is a “generalized -gon”, then is a Tits building modelled on a reflection group of the hyperbolic plane. We give a condition on for to be non enumerable (which is satisfied if is a thick classical generalized -gon). On the other hand,...
Root systems for two dimensional complex reflection groups.
Rotation du sous-espace invariant d’un endomorphisme symétrique de par une perturbation symétrique
Sobre la geometría de la diferencia simétrica.
Some characterization theorems for the discrete holometric space.
Some properties of the discrete holometric space
Some Results on Maps That Factor through a Tree
We give a necessary and sufficient condition for a map deffned on a simply-connected quasi-convex metric space to factor through a tree. In case the target is the Euclidean plane and the map is Hölder continuous with exponent bigger than 1/2, such maps can be characterized by the vanishing of some integrals over winding number functions. This in particular shows that if the target is the Heisenberg group equipped with the Carnot-Carathéodory metric and the Hölder exponent of the map is bigger than...
Some results on metric trees
Using isometric embedding of metric trees into Banach spaces, this paper will investigate barycenters, type and cotype, and various measures of compactness of metric trees. A metric tree (T, d) is a metric space such that between any two of its points there is a unique arc that is isometric to an interval in ℝ. We begin our investigation by examining isometric embeddings of metric trees into Banach spaces. We then investigate the possible images x₀ = π((x₁ + ... + xₙ)/n), where π is a contractive...
Spaces with exceptional fundamental groups.
Spiegelungsgeometrische Darstellung affiner Ebenen auf der Grundlage eines abgeschwächten Schrägspiegelungsbegriffs