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.
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“Im kleinen” is a German expression which means “on a small scale”.
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Bracci, F., Contreras, M.D., Díaz-Madrigal, S. (2020). Carathéodory’s Prime Ends Theory. In: Continuous Semigroups of Holomorphic Self-maps of the Unit Disc. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-36782-4_4
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DOI: https://doi.org/10.1007/978-3-030-36782-4_4
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Online ISBN: 978-3-030-36782-4
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