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Proof of Theorem 8.3. Conformal Transformations of the Canonical Simply-Connected Domains

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Twenty-One Lectures on Complex Analysis

Part of the book series: Springer Undergraduate Mathematics Series ((SUMS))

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Abstract

We are now ready to prove the Riemann Mapping Theorem.

Proof (Theorem 8.3). First of all, by applying a suitable Möbius transformation we can assume that one of the points in \( \overline{\mathbb{C}} \backslash D\ \mathrm{is}\ \infty,\ \mathrm{i.e}. \), that D lies in \( \mathbb{C} \).

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Isaev, A. (2017). Proof of Theorem 8.3. Conformal Transformations of the Canonical Simply-Connected Domains. In: Twenty-One Lectures on Complex Analysis. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-68170-2_21

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