## Plane Domains with Hyperelliptic Double |

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### Contents

THE GEOMETRY AND FUNCTION THEORY OF PLANE DOMAINS WITH HYPER | 7 |

The Greens Function and Harmonic Measures | 30 |

h The Bergman Kernel Function | 42 |

6 other sections not shown

### Common terms and phrases

2g+2 fixed points adjoint analytic and univalent analytic functions anticonformal involution Bergman kernel function boundary components boundary segments canonical horizontal slit Chapter closed orthonormal system closed Riemann surface compute conformal homeomorphism conformal involution conformal mappings conformally equivalent Corollary defined denote differential w^(z)dz domain D(r domain functionals domain in 21 domains with hyperelliptic equation 23 fractional linear transformation genus g Green's function harmonic measures horizontal slit mapping hyperelliptic double hyperelliptic Riemann surface hyperelliptic surface identity induction coefficients kernel function K(z Lemma linear space meromorphic function Nehari 23 Noether's theorem notation Observe obtain parameter space Xn path r(t plane domains point at infinity Proof of Theorem quadratic differentials ramification index real axis real numbers recall Riemann sphere satisfy Schiffer sheet interchange sides of equation suppose surface of genus symmetric Szego kernel function theory theta function uniqueness univalent mapping variational formulas Weierstrass points wy(z