A complete 3-dimensional Blaschke-Santaló diagram

On the Expected Complexity of the 3-dimensional Voronoi Diagram

Elastic energy of a convex body

In this paper a Blaschke-Santaló diagram involving the area, the perimeter and the elastic energy of planar convex bodies is considered. More precisely we give a description of set

Two-dimensional Blaschke Products: Degree Growth and Ergodic Consequences

We study the dynamics of Blaschke products in two dimensions, particularly the rates of growth of the degrees of iterates and the corresponding implications for the ergodic properties of the map.

Infinite Dimensional Universal Subspaces Generated by Blaschke Products

LetH∞ be the Banach algebra of all bounded analytic functions in the unit disk D. A function f ∈ H∞ is said to be universal with respect to the sequence ( z+zn 1+znz )n of noneuclidian translates, if the set {f( z+zn 1+znz ) : n ∈ N} is locally uniformly dense in the set of all holomorphic functions bounded by ||f ||∞. We show that for any sequence of points (zn) in D tending to the boundary th...

A Characterization of Blaschke Addition

A characterization of Blaschke addition as a map between origin-symmetric convex bodies is established. This results from a new characterization of Minkowski addition as a map between origin-symmetric zonoids, combined with the use of Lévy-Prokhorov metrics. A full set of examples is provided that show the results are in a sense the best possible.