## Compact Riemann Surfaces"Although Riemann surfaces are a time-honoured subject, this book is novel in its broad perspective that systematically explores the connections with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole, as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic partial differential equations, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmuller theory. The analytic approach is likewise new, as it is based on the theory of harmonic maps."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved |

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### Contents

Topological Foundations | 1 |

Differential Geometry of Riemann Surfaces | 19 |

Riemann Surfaces | 53 |

Copyright | |

4 other sections not shown

### Other editions - View all

Compact Riemann Surfaces: An Introduction to Contemporary Mathematics Jürgen Jost Limited preview - 2013 |

Compact Riemann Surfaces: An Introduction to Contemporary Mathematics Jürgen Jost Limited preview - 2013 |

Compact Riemann Surfaces: An Introduction to Contemporary Mathematics Jürgen Jost No preview available - 2002 |

### Common terms and phrases

algebraic already apply argument assume Banach space boundary bounded called carries chart choose closed compact Riemann surface complete compute conformal connected consider const constant construct contained continuous converges coordinates Corollary corresponding covering curvature curve defined Definition denote depends derivatives determined differential divisor domain dz dz edge element equation equivalent example Exercises exists fact Finally finitely fixed follows fundamental geodesic geometry given harmonic maps hence holomorphic homeomorphism homotopic hyperbolic metric identified identity integral interior intersection isometry Lemma length linear manifold means meromorphic function namely neighbourhood observe obtain orientation particular path pole polygon precisely Proof prove Remark respect result satisfies sequence sides solution space structure Suppose Theorem theory topological torus transformation unique vanish weakly yields zero