Sharp Lipschitz constants for the distance ratio metric

Abstract

We study expansion/contraction properties of some common classes of mappings of the Euclidean space Rn, n ≥ 2, with respect to the distance ratio metric. The first main case is the behavior of Möbius transformations of the unit ball in Rn onto itself. In the second main case we study the polynomials of the unit disk onto a subdomain of the complex plane. In both cases sharp Lipschitz constants are obtained.