Asymptotics of convex sets in Euclidean and hyperbolic spaces (Q1002243)

Motivated by the problem to find analogues of Dvoretsky's theorem in high-dimensional hyperbolic spaces \(\mathbb H^n\) the author shows that the intersection of a nonempty interior convex set \(C\) of finite volume in \(\mathbb H^n\) with the ideal boundary of \(\mathbb H^n\) has Minkowski dimension at most \((n-1)/2\), and that this bound is sharp for some \(n\). For any \(k\leq (n-1)/2\) it is proved that there is a \(k\)-dimensional plane through any given point \(p\) of \(C\) having bounded diameter.