A note on spherical derivatives and normal families

Jürgen Grahl; Shahar Nevo

A note on spherical derivatives and normal families

Complex Variables 2010-10-25 v1

Authors: Jürgen Grahl , Shahar Nevo

Abstract

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$.

Keywords

univalent functions

Cite

@article{arxiv.1010.4654,
  title  = {A note on spherical derivatives and normal families},
  author = {Jürgen Grahl and Shahar Nevo},
  journal= {arXiv preprint arXiv:1010.4654},
  year   = {2010}
}

Comments

12 pages

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