Sharp Lipschitz constants for the distance ratio metric

Details Sharp Lipschitz constants for the distance ratio metric Sharp Lipschitz constants for the distance ratio metric

2012-02-29

arxiv.org/abs/1202.6565v2

Mathematics

Complex Variables

14 pages, 1 figure

Scientific paper

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 M\"obius transformations of the unit ball ${\mathbb B}^n$ in ${\mathbb R}^n$ onto itself. In the second main case we study the behavior of bounded analytic functions or polynomials of the unit disk. In both cases sharp constants are obtained.

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