Normal families of Möbius maps

Beardon, Alan; Minda, David and Short, Ian (2020). Normal families of Möbius maps. Computational Methods and Function Theory (In press).

Abstract

Several necessary and sufficient conditions for a family of Möbius maps to be a normal family in the extended complex plane are established. Each of these conditions involves collections of two or three points which may vary with the Möbius 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 Möbius maps in terms of the average value of the reciprocal of the chordal derivative.

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