On equicontinuity of homeomorphisms with finite distortion in the plane

Details On equicontinuity of homeomorphisms with finite distortion in the plane On equicontinuity of homeomorphisms with finite distortion in the plane

2010-12-21

arxiv.org/abs/1012.4590v1

Mathematics

Complex Variables

18 pages

Scientific paper

It is stated equicontinuity and normality of families $\frak{F}^{\Phi}$ of the so--called homeomorphisms with finite distortion on conditions that $K_{f}(z)$ has finite mean oscillation, singularities of logarithmic type or integral constraints of the type $\int\Phi\left(K_{f}(z)\right)dx\,dy<\infty$ in a domain $D\subset{\C}.$ It is shown that the found conditions on the function $\Phi$ are not only sufficient but also necessary for equicontinuity and normality of such families of mappings.

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