Endliche minkowskische Ebenen von Charakteristik ... 2.
Equilateral triangles and continuous curves
Euclidean quasiconvexity.
Extension and reconstruction theorems for the Urysohn universal metric space
We prove some extension theorems involving uniformly continuous maps of the universal Urysohn space. As an application, we prove reconstruction theorems for certain groups of autohomeomorphisms of this space and of its open subsets.
Flächengleichheit und Cavalierische Gleichheit von Dreiecken.
Galilean plane with commutative and nonlinear geometry.
Generators of the unitary group of characteristic 2.
Geometry without topology as a new conception of geometry.
G-Hüllen metrischer Teilräume.
Gluing Hyperconvex Metric Spaces
We investigate how to glue hyperconvex (or injective) metric spaces such that the resulting space remains hyperconvex. We give two new criteria, saying that on the one hand gluing along strongly convex subsets and on the other hand gluing along externally hyperconvex subsets leads to hyperconvex spaces. Furthermore, we show by an example that these two cases where gluing works are opposed and cannot be combined.
Gromov Minimal Fillings for Finite Metric Spaces
"Höhenschnittpunkte" für n-Simplizes.
Introduction aux géométries de Hilbert
Invariance of regularity conditions under definable, locally Lipschitz, weakly bi-Lipschitz mappings
We describe the notion of a weakly Lipschitz mapping on a stratification. We also distinguish a class of regularity conditions that are in some sense invariant under definable, locally Lipschitz and weakly bi-Lipschitz homeomorphisms. This class includes the Whitney (B) condition and the Verdier condition.
Invariant resistive networks in Euclidean spaces and their relation to geometry
Geometric properties of finite systems of homogeneous resistive wire segments in a Euclidean -space are studied in the case that the absorption of energy of such a system in an arbitrary linear electrical field is invariant under any orthogonal transformation of the system.
Isometries of spaces of convex compact subsets of globally non-positively Busemann curved spaces
We consider the Hausdorff metric on the space of compact convex subsets of a proper, geodesically complete metric space of globally non-positive Busemann curvature in which geodesics do not split, and characterize their surjective isometries. Moreover, an analogous characterization of the surjective isometries of the space of compact subsets of a proper, uniquely geodesic, geodesically complete metric space in which geodesics do not split is given.
Isometries of systolic spaces
We provide a classification of isometries of systolic complexes corresponding to the classification of isometries of CAT(0)-spaces. We prove that any isometry of a systolic complex either fixes the barycentre of some simplex (elliptic case) or stabilizes a thick geodesic (hyperbolic case). This leads to an alternative proof of the fact that finitely generated abelian subgroups of systolic groups are undistorted.
Les géométries de Hilbert sont à géométrie locale bornée
On montre que la géométrie de Hilbert d’un domaine convexe de est à géométrie locale bornée c-à-d que pour un rayon fixé, toutes les boules sont bilipschitz à un domaine de euclidien. On en déduit que si la géométrie de Hilbert est hyperbolique au sens de Gromov, alors le bas de son spectre est strictement positif. On donne un contre-exemple en dimension trois qui montre que la réciproque n’est pas vraie pour les géométries de Hilbert non planes.
Metric characterizations of hyperbolic and Euclidean spaces
Metric trees in the Gromov--Hausdorff space
Using the wedge sum of metric spaces, for all compact metrizable spaces, we construct a topological embedding of the compact metrizable space into the set of all metric trees in the Gromov--Hausdorff space with finite prescribed values. As its application, we show that the set of all metric trees is path-connected and all its nonempty open subsets have infinite topological dimension.