Codimension-1 simplices in divisible convex domains

Divisible Uniserial Modules over Valuation Domains

Approximation of convex bodies by inscribed simplices of maximum volume

The Banach-Mazur distance between an arbitrary convex body and a simplex in Euclidean n-space En is at most n+2. We obtain this estimate as an immediate consequence of our theorem which says that for an arbitrary convex body C in En and for any simplex S of maximum volume contained in C the homothetical copy of S with ratio n + 2 and center in the barycenter of S contains C . In general, this r...

Tverberg’s Theorem and Shadows of Simplices and Convex Bodies

Helge Tverberg published more than forty years ago his original proof of the theorem which has been widely acclaimed and today bears his name. This beautiful result has been one of the most celebrated results of discrete geometry and, together with its relatives, still remains a central and one of the most intriguing results of geometric combinatorics. Here we give a reasonably non-technical pr...

Quasihyperbolic geodesics in convex domains

We show that quasihyperbolic geodesics exist in convex domains in reflexive Banach spaces and that quasihyperbolic geodesics are quasiconvex in the norm metric in convex domains in all normed spaces. 2000 Mathematics Subject Classification: 30C65

Hyperbolicity in Unbounded Convex Domains

We provide several equivalent characterizations of Kobayashi hyperbolicity in unbounded convex domains in terms of peak and anti-peak functions at infinity, affine lines, Bergman metric and iteration theory.