A Beckmann Quarles Type Theorem for Plane Lorentz Transformations.
A synthetic approach to the taxicab circles.
Averaging at any level.
Bi-Lipschitz embeddings into low-dimensional Euclidean spaces
Gromov Minimal Fillings for Finite Metric Spaces
Integral distance on a Lipschitz Riemannian manifold.
Isometrien in normierten Räumen.
On a problem for isometric mappings of posed by Th. M. Rassias.
On some properties of the metric dimension
On the Lifshits Constant for Hyperspaces
The Lifshits theorem states that any k-uniformly Lipschitz map with a bounded orbit on a complete metric space X has a fixed point provided k < ϰ(X) where ϰ(X) is the so-called Lifshits constant of X. For many spaces we have ϰ(X) > 1. It is interesting whether we can use the Lifshits theorem in the theory of iterated function systems. Therefore we investigate the value of the Lifshits constant for several classes of hyperspaces.
On the relation between ordered sets and Lorentz--Minkowski distances in real inner product spaces.
Producto, convexificación y completación de espacios métricos generalizados y probabilísticos.
En 1967 E. Trillas introdujo la noción de espacio métrico generalizado, al considerar métricas abstractas valoradas en semigrupos ordenados, unificando con este punto de vista algebraico-reticular las estructuras métricas reales de M. Fréchet ([5]) y los espacios métricos probabilísticos de K. Menger ([6]) (así como los espacios Booleanos de Blumenthal ([4]) y las métricas naturales definidas en grupos ordenados). En el presente artículo se abordan los problemas de la topología del orden, del producto,...
Rigidity and Energy.
Sphere-and-Point Incidence Relations in High Dimensions with Applications to Unit Distances and Furthest-Neighbor Pairs.
The CC-version of Stewart's theorem.
Transformations of Robertson-Walker spacetimes preserving separation zero.
Zone and double zone diagrams in abstract spaces
A zone diagram of order n is a relatively new concept which was first defined and studied by T. Asano, J. Matoušek and T. Tokuyama. It can be interpreted as a state of equilibrium between n mutually hostile kingdoms. Formally, it is a fixed point of a certain mapping. These authors considered the Euclidean plane with finitely many singleton-sites and proved the existence and uniqueness of zone diagrams there. In the present paper we generalize this concept in various ways. We consider general sites...
О единичных базах евклидовой метрики.
О некоторых минимальных условиях определяющих изометрические и подобные отображения.
Пример одномерного жесткого множества на плоскости