Normal Families of Mobius Maps

摘要

Several necessary and sufficient conditions for a family of Mobius maps to be a normal family in the extended complex plane C-infinity are established. Each of these conditions involves collections of two or three points which may vary with the Mobius maps in the family, provided the points satisfy a uniform separation condition. In addition, we derive a sufficient condition for the normality of a family of Mobius maps in terms of the average value of the reciprocal of the chordal derivative.