Arrangements of Lines with a Minimum Number of Triangles Are Simple.
Asphericity of shadows of a convex body.
Asymptotes and Projections of Convex Sets.
Asymptotic approximation of smooth convex bodies by polytopes.
Asymptotic behaviour of averages of k-dimensional marginals of measures on ℝⁿ
We study the asymptotic behaviour, as n → ∞, of the Lebesgue measure of the set for a random k-dimensional subspace E ⊂ ℝⁿ and an isotropic convex body K ⊂ ℝⁿ. For k growing slowly to infinity, we prove it to be close to the suitably normalised Gaussian measure in of a t-dilate of the Euclidean unit ball. Some of the results hold for a wider class of probabilities on ℝⁿ.
Asymptotic estimates for best and stepwise approximation of convex bodies III.
Asymptotic estimates for best and stepwise approximation of convex bodies I.
Asymptotic estimates for best and stepwise approximation of convex bodies II.
Asymptotic mean values of Gaussian polytopes.
Asymptotics of cross sections for convex bodies.
Asymptotische Berührung -ter Ordnung konvexer Mengen
In der Arbeit geht es um die Charakteristik des allgemeinen Begriffs der asymptotischen Berührung von solchen abgeschlossenen, konvexen Mengen in , wo ihr Abstand gleich Null und ihr Durchschnitt leer ist. Es wird gezeigt, dass unter diesem Umstand man dem fraglichen Mengenpaar ein Tripel von natürlichen Zahlen (die Ordnung der Berührung, der Grad der Berührung und die Diemnsion des zugehörigen asymptotischen, linearen Raumes), welches eine Charakteristik dieser Berührung darstellt, eindeutig zuordnen...
Asymptotische Berührung von zwei konvexen Mengen in (bestimmter) Richtung
Autour de l'inégalité de Brunn-Minkowski
Average decay of Fourier transforms and geometry of convex sets.
Let B be a convex body in R2, with piecewise smooth boundary and let ^χB denote the Fourier transform of its characteristic function. In this paper we determine the admissible decays of the spherical Lp averages of ^χB and we relate our analysis to a problem in the geometry of convex sets. As an application we obtain sharp results on the average number of integer lattice points in large bodies randomly positioned in the plane.
Averaging at any level.
Axiomatization and undecidability results for linear betweenness relations
Balancing vectors and convex bodies
Let U, V be two symmetric convex bodies in and |U|, |V| their n-dimensional volumes. It is proved that there exist vectors such that, for each choice of signs , one has where . Hence it is deduced that if a metrizable locally convex space is not nuclear, then it contains a null sequence such that the series is divergent for any choice of signs and any permutation π of indices.
Ball versus distance convexity of metric spaces.
Banach spaces which are semi-L-summands in their biduals.
Banach-Mazur distance of central sections of a centrally symmetric convex body.