Compact Riemann Surfaces: An Introduction to Contemporary MathematicsAlthough Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection 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 PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory. The analytic approach is likewise new as it is based on the theory of harmonic maps. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation. |
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Compact Riemann Surfaces: An Introduction to Contemporary Mathematics Jürgen Jost No preview available - 2002 |
Common terms and phrases
a₁ algebraic b₁ bijective boundary c₁ choose compact Riemann surface conformal structure const construct continuous map converges coordinates Corollary covering curvature curve defined Definition denote diffeomorphism divisor dz dz dz² E₁ elliptic equation exists Əzəz finitely fixed points follows fundamental domain fundamental polygon geodesic geodesic arcs geometry harmonic maps Hence holomorphic map holomorphic quadratic differential homeomorphism homotopic homotopy class hyperbolic metric integral intersection isometry L²(N Lemma line bundle linear linearly equivalent manifold meromorphic function Möbius transformation neighbourhood obtain p₁ path pole proof of Theorem prove quadratic differential Riemann-Roch theorem satisfies sequence sides surface of genus Teichmüller space topology torus transformation triangle U₁ uniformization theorem unique vanish vertex w₁ zero