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.
A sequence of inequalities for certain sets of concurrent cevians.
A sequential iteration algorithm with non-monotoneous behaviour in the method of projections onto convex sets
The method of projections onto convex sets to find a point in the intersection of a finite number of closed convex sets in a Euclidean space, may lead to slow convergence of the constructed sequence when that sequence enters some narrow “corridor” between two or more convex sets. A way to leave such corridor consists in taking a big step at different moments during the iteration, because in that way the monotoneous behaviour that is responsible for the slow convergence may be interrupted. In this...
A sharp estimate of the number of integral points in a 4-dimensional tetrahedra.
A sharp isoperimetric inequality in the plane
We show that among all the convex bounded domain in having an assigned Fraenkel asymmetry index, there exists only one convex set (up to a similarity) which minimizes the isoperimetric deficit. We also show how to construct this set. The result can be read as a sharp improvement of the isoperimetric inequality for convex planar domain.
A sharpening of a discrete analog of Wirtinger's and isoperimetric inequalities
A sharpening of a discrete case of Wirtinger's inequality is given. It is then used to sharpen the isoperimetric unequality for polygons.
A sharpening of discrete analogues of Wirtinger's inequality
A short introduction to shadows of 4-manifolds
We give a self-contained introduction to the theory of shadows as a tool to study smooth 3-manifolds and 4-manifolds. The goal of the present paper is twofold: on the one hand, it is intended to be a shortcut to a basic use of the theory of shadows, on the other hand it gives a sketchy overview of some of the most recent results on shadows. No original result is proved here and most of the details of the proofs are left out.
A short proof, based on mixed volumes, of Liggett's theorem on the convolution of ultra-logconcave sequences.
A short proof of Dvoretzky's theorem on almost spherical sections of convex bodies
A short proof of rigidity of convex polytopes.
A Simple and Relatively Efficient Triangulation of the n-Cube.
A simple geometrie proof of a theorem for starshaped unions of convex sets