Normal Families of Möbius Maps

Beardon, Alan; Minda, David and Short, Ian (2020). Normal Families of Möbius Maps. Computational Methods and Function Theory, 20 pp. 523–538.

DOI: https://doi.org/10.1007/s40315-020-00328-7

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.

Viewing alternatives

Metrics

Item Actions

Export

You can export this page using these formats Digital Object Identifier - DOI

About

• Item ORO ID
• 69886
• Item Type
• Journal Item
• ISSN
• 1617-9447
• Keywords
• chordal derivative; meromorphic; Möbius maps; normal families
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2020 Springer
• Depositing User
• Ian Short