Carathéodory's Theorem

If Omega_1 and Omega_2 are bounded domains, partialOmega_1, partialOmega_2 are Jordan curves, and phi:Omega_1->Omega_2 is a conformal mapping, then phi (respectively, phi^(-1)) extends one-to-one and continuously to partialOmega_1 (respectively, partialOmega_2).

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Krantz, S. G. Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 152, 1999.

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Carathéodory's Theorem

Cite this as:

Weisstein, Eric W. "Carathéodory's Theorem." From MathWorld--A Wolfram Web Resource.

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