Iterations of Minkowski Valuations

Abstract

It is shown that for any sufficiently regular even Minkowski valuation Φ which is homogeneous and intertwines rigid motions, and for any convex body K in a smooth neighborhood of the unit ball, there exists a sequence of positive numbers (γ m ) ∞ m=1 such that (γ m Φ m K) ∞ m=1 converges to the unit ball with respect to the Hausdorff metric.