A note on spherical derivatives and normal families

Details A note on spherical derivatives and normal families A note on spherical derivatives and normal families

2010-10-22

arxiv.org/abs/1010.4654v1

Mathematics

Complex Variables

12 pages

Scientific paper

We show that a family of meromorphic functions in the unit disk $\dk$ whose
spherical derivatives are uniformly bounded away from zero is normal.
Furthermore, we show that for each $f$ meromorphic in $\dk$ we have
$\inf_{z\in\dk} f^#(z)\le \frac{1}{2}$$ where $f^#$ denotes the spherical
derivative of $f$.

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