On the curvature of nonregular saddle surfaces in the hyperbolic and spherical three-space.
On the Curvatures of Convex Bodies.
On the curves of constant relative width
On the decomposition of a vector space in the sum of a convex set and a subspace
On the diameter of matroid ports.
On the diffeomorphic type of the complement to a line arrangement in a projective plane
We show that the diffeomorphic type of the complement to a line arrangement in a complex projective plane P 2 depends only on the graph of line intersections if no line in the arrangement contains more than two points in which at least two lines intersect. This result also holds for some special arrangements which do not satisfy this property. However it is not true in general, see [Rybnikov G., On the fundamental group of the complement of a complex hyperplane arrangement, Funct. Anal. Appl., 2011,...
On the differentiation of convex functions
On the differentiation of convex functions in finite and infinite dimensional spaces
On the Difficulty of Triangulating Three-Dimensional Nonconvex Polyhedra.
On the Erdös-Debrunner inequality.
On the estension of Lipschitz functions with respect to two Hilbert norms and two Lipschitz conditions
On the Euler Characteristic in Spaces with a Separability Property.
On the Euler Characteristic of Finite Unions of Convex Sets.
On the Exact Constant in the Quantitative Steinitz Theorem in the Plane.
On the existence of wavelets for non-expansive dilation matrices.
Sets which simultaneously tile Rn by applying powers of an invertible matrix and translations by a lattice are studied. Diagonal matrices A for which there exist sets that tile by powers of A and by integer translations are characterized. A sufficient condition and a necessary condition on the dilations and translations for the existence of such sets are also given. These conditions depend in an essential way on the interplay between the eigenvectors of the dilation matrix and the translation lattice...
On the Expected Number of k-Sets.
On the Face-Vector of a 5-Valent Convex 3-Polytope
On the face-vectors of trivalent convex polyhedra
On the Fundamental Group of self-affine plane Tiles
Let be an expanding matrix, a set with elements and define via the set equation . If the two-dimensional Lebesgue measure of is positive we call a self-affine plane tile. In the present paper we are concerned with topological properties of . We show that the fundamental group of is either trivial or uncountable and provide criteria for the triviality as well as the uncountability of . Furthermore, we give a short proof of the fact that the closure of each component of is a locally...
On the general Brunn-Minkowski theorem.