On equicontinuity of homeomorphisms with finite distortion in the plane
It is stated equicontinuity and normality of families $\frak{F}^Φ$ 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 $\intΦ\left(K_{f}(z)\right)dx\,dy<\infty$ in a domain $D\subset{\C}.$ It is shown that the found conditions on the function $Φ$ are not only sufficient but also necessary for equicontinuity and normality of such families of mappings.
math.CV↗