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Carathéodory’s Prime Ends Theory

  • Filippo BracciEmail author
  • Manuel D. Contreras
  • Santiago Díaz-Madrigal
Chapter
  • 34 Downloads
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

The aim of this chapter is to introduce prime ends and the Carathéodory topology of simply connected domains and see how impressions of prime ends are related to unrestricted limits and principal parts of prime ends can be used to understand the non-tangential behavior of univalent functions. Finally, we prove Carathéodory’s extension theorems.

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Filippo Bracci
    • 1
    Email author
  • Manuel D. Contreras
    • 2
  • Santiago Díaz-Madrigal
    • 2
  1. 1.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomaItaly
  2. 2.Departamento de Matemática Aplicada II and IMUSUniversidad de SevillaSevillaSpain

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