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Area theorem (conformal mapping) : ウィキペディア英語版 | Area theorem (conformal mapping) In the mathematical theory of conformal mappings, the area theorem gives an inequality satisfied by the power series coefficients of certain conformal mappings. The theorem is called by that name, not because of its implications, but rather because the proof uses the notion of area. ==Statement== Suppose that is analytic and injective in the punctured open unit disk and has the power series representation : then the coefficients satisfy :
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