Abstract
In this chapter a number of results on conformal equivalence for simply connected regions are presented. The first section discusses elementary information and examples. The next three sections present the basics of the theory of prime ends for the study of the boundary behavior of Riemann maps. This will be used in §5 to show that the Riemann map from the unit disk onto the inside of a Jordan curve can be extended to a homeomorphism on the closure of the disk. The chapter then closes with a discussion of the family of all functions that are one-to-one on a simply connected region.
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© 1995 Springer Science+Business Media New York
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Conway, J.B. (1995). Conformal Equivalence for Simply Connected Regions. In: Functions of One Complex Variable II. Graduate Texts in Mathematics, vol 159. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0817-4_2
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DOI: https://doi.org/10.1007/978-1-4612-0817-4_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6911-3
Online ISBN: 978-1-4612-0817-4
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