On Two Finite Covering Problems of Bambah, Rogers, Woods and Zassenhaus.
On unit balls and isoperimetrices in normed spaces
The purpose of this paper is to continue the investigations on the homothety of unit balls and isoperimetrices in higher-dimensional Minkowski spaces for the Holmes-Thompson measure and the Busemann measure. Moreover, we show a strong relation between affine isoperimetric inequalities and Minkowski geometry by proving some new related inequalities.
On Weak Tail Domination of Random Vectors
Motivated by a question of Krzysztof Oleszkiewicz we study a notion of weak tail domination of random vectors. We show that if the dominating random variable is sufficiently regular then weak tail domination implies strong tail domination. In particular, a positive answer to Oleszkiewicz's question would follow from the so-called Bernoulli conjecture. We also prove that any unconditional logarithmically concave distribution is strongly dominated by a product symmetric exponential measure.
One functional-analytical idea by Alexandrov in convex geometry.
Optimierung konstant belegter Ovale und ein Hyperbel-Schnittsatz
Optimizing geometric measures for fixed minimal annulus and inradius.
Packing of 180 equal circles on a sphere.
Penny-Packing and Two-Dimensional Codes.
Poincaré Inequalities and Moment Maps
We discuss a method for obtaining Poincaré-type inequalities on arbitrary convex bodies in . Our technique involves a dual version of Bochner’s formula and a certain moment map, and it also applies to some non-convex sets. In particular, we generalize the central limit theorem for convex bodies to a class of non-convex domains, including the unit balls of -spaces in for .
Quelques exemples d'application du transport de mesure en géométrie euclidienne et riemannienne
Radial Minkowski additive operators
We give some characterizations for radial Minkowski additive operators and prove a new characterization of balls. Finally, we show the property of radial Minkowski homomorphism.
Radii of simplices and some applications to geometric inequalities.
Random polytopes and the volume-product of symmetric convex bodies.
Redundance of vertices of the cube relatively to its minimal ellipsoid.
Relative isodiametric inequalities.
Remarks on the closest packing of convex discs.
Remarks on the Isoperimetric Inequality for Multiply-connected H-Surfaces.
Repeated Angles in E4 .
Sharpening on Mircea's inequality.
Shift inequalities of Gaussian type and norms of barycentres
We derive the equivalence of different forms of Gaussian type shift inequalities. This completes previous results by Bobkov. Our argument strongly relies on the Gaussian model for which we give a geometric approach in terms of norms of barycentres. Similar inequalities hold in the discrete setting; they improve the known results on the so-called isodiametral problem for the discrete cube. The study of norms of barycentres for subsets of convex bodies completes the exposition.