## Quasiconformal mappings and Riemann surfaces |

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### Contents

Basic Extremal Problems in the Theory | 53 |

Quasiconformal Mappings with a Given | 111 |

3 An approximation theorem for analytic functions | 124 |

Copyright | |

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### Common terms and phrases

Ahlfors analogous annulus arbitrary assertion assume Beltrami differential boundary Chapter circle class Q(E closed surface coefficients compact completes the proof complex dilatation components conformal automorphisms conformal mapping conformally equivalent constant converges corresponding curve denote disk divisor dudv dxdy elliptic elements equation estimate exists extremal mapping finite number finite type fixed points follows Fuchsian group fundamental polygon fundamental region genus g group G half-plane holomorphic functions homeo homotopic inequality invariant isomorphism Kleinian groups Lemma Let us define Let us look Let us show linear marked surfaces meromorphic meromorphic function moduli morphic morphisms neighborhood norm obtain parameter plane point z0 proof of Theorem properties quadratic differentials quasicircle quasiconformal automorphism quasiconformal homeomorphism quasiconformal mappings respect satisfy the condition Schwarzian derivative simply-connected solution sufficiently small Suppose surface of genus transformations type g unique univalent univalent analytic functions universal covering variational formula virtue zero