We formulate and discuss a conjecture concerning lower bounds for norms of log-concave vectors, which generalizes the classical Sudakov minoration principle for Gaussian vectors. We show that the conjecture holds for some special classes of log-concave measures and some weaker forms of it are satisfied in the general case. We also present some applications based on chaining techniques.
In questa Nota diamo una caratterizzazione dell'insieme di tutti i flocks lineari della quadrica iperbolica assolutamente irriducibile in .
In this paper, we define the supersolvable order of hyperplanes in a supersolvable arrangement, and obtain a class of inductively free arrangements according to this order. Our main results improve the conclusion that every supersolvable arrangement is inductively free. In addition, we assert that the inductively free arrangement with the required induction table is supersolvable.
A problem of finding a system of proportionally located parallel supporting hyperplanes of a family of connected compact sets is analyzed. A special attention is paid to finding a common supporting halfspace. An existence theorem is proved and a method of solution is proposed.
The aim of this paper is to give a classification of the right-angled hyperbolic hexagons in the real hyperbolic space , by using a quaternionic distance between geodesics in .
Siano , sottoinsiemi convessi, chiusi e limitati di uno spazio normato , con le frontiere , . Dimostriamo che , dove è la metrica di Hausdorff tra sottoinsiemi chiusi di . Studiamo inoltre la continuità e la semicontinuità superiore ed inferiore di una multifunzione di tipo «frontiera».
Un polyèdre hyperbolique semi-idéal est un polyèdre dont les sommets sont dans l’espace hyperbolique ou à l’infini. Un polyèdre hyperbolique hyperidéal est, dans le modèle projectif, l’intersection de avec un polyèdre projectif dont les sommets sont tous en dehors de et dont toutes les arêtes rencontrent . Nous classifions les polyèdres semi-idéaux en fonction de leur métrique duale, d’après les résultats de Rivin dans [8] (écrit avec C.D.Hodgson) et [7]. Nous utilisons ce résultat pour retrouver...