Sharp Lipschitz constants for the distance ratio metric

Abstract

We study expansion/contraction properties of some common classes of mappings of the Euclidean space ${\mathbb{R}}^n,n\ge 2,$ with respect to the distance ratio metric. The first main case is the behavior of Möbius transformations of the unit ball in ${\mathbb{R}}^n$ 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.

14 pages

References in corpus (1)

• Local Convexity Properties of Quasihyperbolic Balls in Punctured Space

Cited by in corpus (1)

• On lengths, areas and Lipschitz continuity of polyharmonic mappings