Inversion formulas for the Dunkl intertwining operator and its dual on spaces of functions and distributions.
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.
Konvexe Fundamentalpolyeder und einfache D-V-Zellen für 29 Raumgruppen, die Coxetersche Spiegelungsuntergruppen enthalten
L'aire systolique conforme des groupes cristallographiques du plan
Nous établissons des inégalités isosystoliques optimales pour les 17 orbifolds plates en dimension 2 (analogues à l’inégalité classique de Loewner pour le tore), ainsi que pour les quotients du plan hyperbolique par les groupes du triangle.
Les arrangements d'hyperplans : un chapitre de géométrie combinatoire
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.
L'Hospital-type rules for monotonicity, and the Lambert and Saccheri quadrilaterals in hyperbolic geometry.
Linearly rigid metric spaces and the embedding problem
We consider the problem of isometric embedding of metric spaces into Banach spaces, and introduce and study the remarkable class of so-called linearly rigid metric spaces: these are the spaces that admit a unique, up to isometry, linearly dense isometric embedding into a Banach space. The first nontrivial example of such a space was given by R. Holmes; he proved that the universal Urysohn space has this property. We give a criterion of linear rigidity of a metric space, which allows us to give a...
Lower levels of Euclidean planes.
Mappings of Galois planes preserving the unit Euclidean distance.
Mathematics and crystallography.
Metric characterizations of hyperbolic and Euclidean spaces
Metrics and tolerances
Metrische Räume mit einer Elementarlänge.
Minimal dimensions for flat manifolds with prescribed holonomy.
Note on angle-preserving mappings.
Notes per a un estudi de la geometría sobre grups involutius.
O jednom zovšeobecnení Menelaovej a Cevovej vety
On a general principle in geometry that leads to functional equations.