Abstract
In this chapter we study conformal maps between domains in the extended complex plane. These maps are one-to-one meromorphic functions. Our goal is characterize all simply connected domains in the complex plane. The first two sections of this chapter study the action of a quotient of the group of two-by-two nonsingular complex matrices on the extended complex plane
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© 2007 Springer Science+Business Media, LLC
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Gilman, J.P., Kra, I., Rodríguez, R.E. (2007). Conformal Equivalence. In: Complex Analysis. Graduate Texts in Mathematics, vol 245. Springer, New York, NY. https://doi.org/10.1007/978-0-387-74715-6_8
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DOI: https://doi.org/10.1007/978-0-387-74715-6_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-74714-9
Online ISBN: 978-0-387-74715-6
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