Distortion of normalized quasiconformal mappings

Details Distortion of normalized quasiconformal mappings Distortion of normalized quasiconformal mappings

2008-08-08

arxiv.org/abs/0808.1219v4

Mathematics

Complex Variables

20 pages

Scientific paper

Quasiconformal homeomorphisms of the whole space of ${\mathbb R}^n,$ onto itself normalized at one or two points are studied. In particular, the case when the maximal dilatation tends to 1 is in the focus. Our methods make use of an asymptotically sharp bound for quasisymmetry and generalized Bernoulli type inequality. In addition, we prove sharp result for the behavior of the quasihyperbolic metric under quasiconformal maps.

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