## Univalent functions |

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### Contents

Some basic results | 9 |

Some special classes | 35 |

The Grunsky inequality | 56 |

Copyright | |

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### Common terms and phrases

Ahlfors analytic and univalent angle angular derivative angular limit apply Theorem assume Bieberbach conjecture Bloch function boundary bounded choose compact component conformal mapping consider constant converges convex Corollary deduce define denote Diagram diam disjoint disk domain G equality holds estimate exists extremal function finite function f(z Furthermore Grunsky coefficients Grunsky inequality Hayman Hence it follows homeomorphism image domain implies inner domain integral intersect Jenkins normalization Jordan arc Koebe distortion theorem Koebe function Let f(z Let G locally connected locally uniformly Loewner chain Math meromorphic Moebius transformation neighbourhood obtain odd function orthogonal trajectory outer domain pole of order Pommerenke prime end Problems proof of Theorem prove quadratic differential result satisfies Schiffer differential equation schlicht functions Section 1.2 Show simply connected simply connected domain starlike functions trajectory arcs univalent functions zero