Overview

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.

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9783540330653

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

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