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.
Asymptotic volume formulae and hyperbolic ball packing.
Asymptotic-group analysis of algebraic equations.
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
Atomic surfaces, tilings and coincidences II. Reducible case
The atomic surfaces of unimodular Pisot substitutions of irreducible type have been studied by many authors. In this article, we study the atomic surfaces of Pisot substitutions of reducible type.As an analogue of the irreducible case, we define the stepped-surface and the dual substitution over it. Using these notions, we give a simple proof to the fact that atomic surfaces form a self-similar tiling system. We show that the stepped-surface possesses the quasi-periodic property, which implies that...
Au bord de certains polyèdres hyperboliques
Le cadre de cet article est celui des groupes et des espaces hyperboliques de M. Gromov. Il est motivé par la question suivante : comment différencier deux groupes hyperboliques à quasi-isométrie près ? On illustre ce problème en détaillant un exemple de M. Gromov issu de Asymptotic invariants for infinite groups. On décrit une famille infinie de groupes hyperboliques, deux à deux non quasi-isométriques, de bord la courbe de Menger. La méthode consiste à étudier leur structure quasi-conforme au...
Ausbohrung von Rhomben
Automorphismen von polyedrischen Graphen.
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