Compact Riemann Surfaces

1. Front Matter

   Pages I-XVI

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2. Topological Foundations

   • Jürgen Jost

   Pages 1-17

3. Differential Geometry of Riemann Surfaces

   • Jürgen Jost

   Pages 19-80

4. Harmonic Maps

   • Jürgen Jost

   Pages 81-160

5. Teichmüller Spaces

   • Jürgen Jost

   Pages 161-187

6. Geometric Structures on Riemann Surfaces

   • Jürgen Jost

   Pages 189-267

7. Back Matter

   Pages 269-281

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Although 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.

• Meromorphic function
• Riemann surfaces
• Riemann-Roch Theorem
• Schwarz lemma
• Teichmüller theory
• diffeomorphism
• differential geometry
• harmonic maps
• hyberbolic geometry
• hyperbolic geometry
• manifold

From the reviews:

"Compact Riemann Surfaces: An Introduction to Contemporary Mathematics starts off with a wonderful Preface containing a good deal of history, as well as Jost’s explicit dictum that there are three foci around which the whole subject revolves … . Jost’s presentation is quite accessible, modulo a lot of diligence on the part of the reader. It’s a very good and useful book, very well-written and thorough." (Michael Berg, MathDL, April, 2007)

• Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

  Jürgen Jost

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