On the Tetrahedroid as a particular case of the 16-nodal quartic surface.
On the volume of a symmetric tetrahedron in hyperbolic and spherical spaces.
On the volume of hyperbolic polyhedra.
On the volume of unbounded polyhedra in the hyperbolic space.
On the volumes of hyperbolic 5-orthoschemes and the Trilogarithm.
On universal groups and three-manifolds.
On volumes of arithmetic quotients of
We apply G. Prasad’s volume formula for the arithmetic quotients of semi-simple groups and Bruhat-Tits theory to study the covolumes of arithmetic subgroups of . As a result we prove that for any even dimension there exists a unique compact arithmetic hyperbolic -orbifold of the smallest volume. We give a formula for the Euler-Poincaré characteristic of the orbifolds and present an explicit description of their fundamental groups as the stabilizers of certain lattices in quadratic spaces. We...
On -distance in -dimensional space.
Optimierung konstant belegter Ovale und ein Hyperbel-Schnittsatz
Packing lines, planes, etc.: Packings in Grassmannian spaces.
Parabeln mit gemeinsamen isotropem Krümmungskreis.
"Paradoxe" Zerlegung Euklidischer Räume.
Parallelbeleuchtung konvexer Körper mit glatten Rändern
Parallelograms inscribed in a curve having a circle as π/2-isoptic
Jean-Marc Richard observed in [7] that maximal perimeter of a parallelogram inscribed in a given ellipse can be realized by a parallelogram with one vertex at any prescribed point of ellipse. Alain Connes and Don Zagier gave in [4] probably the most elementary proof of this property of ellipse. Another proof can be found in [1]. In this note we prove that closed, convex curves having circles as π/2-isoptics have the similar property.
Partitioning Euclidean Space.
Petrie-Coxeter maps revisited.
Placing and moving spheres in the gaps of a cylinder packing.
Planes with analogues to Euclidean angular bisectors.
Pointed -surfaces
Let be a Riemann surface. Let be the -dimensional hyperbolic space and let be its ideal boundary. In our context, a Plateau problem is a locally holomorphic mapping . If is a convex immersion, and if is its exterior normal vector field, we define the Gauss lifting, , of by . Let be the Gauss-Minkowski mapping. A solution to the Plateau problem is a convex immersion of constant Gaussian curvature equal to such that the Gauss lifting is complete and . In this paper, we show...
Point-reflections in metric plane.