A purely combinatorial proof of the Hadwiger Debrunner conjecture.
A quantitative isoperimetric inequality in n-dimensional space.
A quantitative Steinitz' theorem.
A quantitative version of the isoperimetric inequality : the anisotropic case
We state and prove a stability result for the anisotropic version of the isoperimetric inequality. Namely if is a set with small anisotropic isoperimetric deficit, then is “close” to the Wulff shape set.
A reciprocity theorem for domino tilings.
A Rédei type factorization result for a special 2-group.
A Reduction of Lattice Tiling by Translates of a Cubical Cluster.
A refined Brunn-Minkowski inequality for convex sets
A Relation between the Weyl Group W(e8) and Eight-Line Arrangements on a Real Projective Plane
The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006.The Weyl group W(E8) acts on the con guration space of systems of labelled eight lines on a real projective plane. With a system of eight lines with a certain condition, a diagram consisting of ten roots of the root system of type E8 is associated. We have already shown the existence of a W(E8)-equivariant map of the totality of such diagrams to the set of systems of...
A remark about the directed line-elements in the plane
A remark on mixed curvature measures for sets with positive reach.
A Remark to the Paper of H. Hadwiger "Überdeckung des Raumes durch translationsgleiche Punktmengen und Nachbarnzahl".
A representation for volume involving interior reach.
A reverse isoperimetric inequality for convex plane curves.
A rough curvature-dimension condition for metric measure spaces
We introduce and study a rough (approximate) curvature-dimension condition for metric measure spaces, applicable especially in the framework of discrete spaces and graphs. This condition extends the one introduced by Karl-Theodor Sturm, in his 2006 article On the geometry of metric measure spaces II, to a larger class of (possibly non-geodesic) metric measure spaces. The rough curvature-dimension condition is stable under an appropriate notion of convergence, and stable under discretizations as...
A sandwich theorem and Hyers-Ulam stability of affine functions.
A second order -approximation method for constrained optimization problems involving second order invex functions
A new approach for obtaining the second order sufficient conditions for nonlinear mathematical programming problems which makes use of second order derivative is presented. In the so-called second order -approximation method, an optimization problem associated with the original nonlinear programming problem is constructed that involves a second order -approximation of both the objective function and the constraint function constituting the original problem. The equivalence between the nonlinear...
A selection theorem of Helly type and its applications
We prove an abstract selection theorem for set-valued mappings with compact convex values in a normed space. Some special cases of this result as well as its applications to separation theory and Hyers-Ulam stability of affine functions are also given.
A separation theorem for finite families
A seperation property of plane convex sets.